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No, a Christian can never give grace.  What about with God's help?  No, not even then can a Christian give grace to others.

There is much in the realm of theology (that is, "the study of God," in which every Christian should be actively engaged) that is misguided and untruthful.  One of the deceptions leading to falsehood among confessing Christians is the current distorted definition of grace.

Christians use the word grace in a number of different ways.

We wrongfully use it as an excuse for our sin: "Give grace to your brother when he sins.  Who are you to judge them?"

We wrongfully use it as a means to appease others, rather than confront disobedience: "It looks like my child didn't clean up their toys like I told them to.  I will give grace to them and clean them up for him."

We wrongfully use it as a way to escape judgement: "Give me some grace.  I didn't mean to hurt you."

So, what exactly is grace?  And how are Christians wrongfully using this word?

Grace, according to the segment regarding theology from Dictionary.com, has the following meanings:
"The freely given, unmerited love and favor of God."
"The influence or spirit of God operating in humans to regenerate or strengthen them."
"A virtue or excellence of divine origin."
"Also called state of grace, the condition of being in God's favor or one of the elect."
Grace, by theological standards, is always administered by God.  Never is a human mentioned in the definition of grace except as the beneficiary of such unmerited love and favor by the only true God.  By definition, then, it is impossible for a Christian or any human to give grace since we are not God.

What the Bible Says
The word "grace" never appears in the Bible apart from direct connection to God the Father.
"The Child continued to grow and become strong, increasing in wisdom; the grace of God was upon Him" (Luke 2:40).
"And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the one and only begotten from the Father, full of grace and truth.... For the law was given through Moses; grace and truth came through Jesus Christ" (John 1:14, 17).
"The Law came in so that the transgression would increase; but where sin increased, grace abounded all the more, so that, as sin reigned in death, even so grace would reign through righteousness to eternal life through Jesus Christ our Lord" (Romans 5:20-21).
"The God of peace will soon crush Satan under your feet.  The grace of our Lord Jesus Christ be with you" (Romans 16:20).
"And He said to me, 'My grace is sufficient for you, for power is perfected in weakness...'" (2 Corinthians 12:9).
"For by grace you have been saved through faith; and not of yourselves, it is the gift of God..." (Ephesians 2:8).
"... so that being justified by His grace we would be made heirs according to the hope of eternal life" (Titus 3:7).
"Therefore let us draw near with confidence to the throne of grace, so that we may receive mercy and find grace to help in time of need" (Hebrews 4:16).
"But He gives a greater grace.  Therefore it says, 'God is opposed to the proud, but gives grace to the humble'" (James 4:6).
The Human's Sin-Debt
Every debt a human obtains can be adequately paid for out of his own power and influence.   For instance, if a man walks into a store and obtains a shovel, he pays for it with money or trade.  If he does not have the means in which to buy or trade, he can work for it; in effect, trade his labor for the desired object. It is in his power to adequately pay for it. Similarly, if a man hits another man, he obtains the debt of justice, and justice will be paid back to him by the offended or another man. All debts obtained by man can be adequately paid for by man.

All debts, that is, except for the debt of sin.

Sin is the only debt that man is powerless to adequately pay for. Sin is an eternal wrong because it is a wrong committed against an eternal God. Therefore, since man is hopeless and helpless to adequately pay for sin-debt, God - out of His abundant grace - paid the debt for us, for only He could provide a payment satisfactory for the debt of man’s sin. Jesus, obediently out of love for His Father, bore the payment of man’s sin-debt, dying for our sins and, therefore, adequately removing our debt from those who repent and believe. In fact, not only was our debt paid, but man’s place was restored in the kingdom of God - from which Adam and Eve and all humanity were removed when they were banished from the Garden of Eden - as a result of the resurrection of Jesus Christ. He is, therefore, supreme!  It is by His grace that we live.

Grace is not a passive looking over sin (as the earlier, wrongful uses of grace exemplified).  Grace was and is and will be forever an active, powerful feat of death and resurrection, the Righteous purposely taking the sins of the unrighteousness and giving life to those unfit for it and those who could not afford it in their own power.  To ascribe grace as a token given by man unto other men is to not only redefine grace, but also weaken the understanding of the abundant grace that God gave and gives and will give to His people through Jesus Christ.

So, if human beings cannot give grace, can we at least show it?

Christians can exhibit or show grace because Jesus Christ has given grace to the believer through the power of the Gospel.  Yet, showing is very different from giving grace, as the definition of grace does not allow man to give grace.

This inevitably leads to the question of, "How does a Christian show grace?"  The Christian shows grace - shows the regenerate transformation of the sinful soul unto life through the death and resurrection of Jesus Christ - through kindness, love, compassion, mercy, humility, gentleness, self-control, etc.  Still, Christians cannot give grace.  We can only show it through our good works, as they are worked in us through the Spirit of God Himself, the giver of all grace.

A Final Thought on the Matter
In closing, to say (as many Christians such as myself often profess), "I am no longer under the Law, but under grace" is a truthful statement to be sure; however, sometimes we can deceive ourselves into believing that what we are doing is pleasing to God even though it is not - to justify our sin by using grace as a defense against our wrongdoing.  Instead, to say, "I am no longer under the Law, but under grace" is to say, "There was and is and will never be anything I can do to be righteous or earn God's love or favor, for under the Law I am guilty and condemned because I cannot meet the requirements of His holiness.  But thanks be to God who gave us grace through His Son Jesus Christ, that He would die for my sins and be raised to life for my justification, to the glory of God the Father.  Now I am under His grace because of Jesus Christ, no longer dead in my sins and failed attempts at righteousness, but now clothed with His righteousness through God's grace realized in Christ Jesus.  I am now under His lordship and authority - not sin and death - and will serve Him gratefully in return for what He has done."

Brothers and sisters: Let us run with perseverance this Christian life, fully aware of the grace we have been given through Jesus Christ our Lord.

(For further reading on the subject of grace, visit http://www.heresthejoy.com/2012/11/how-can-i-give-grace/.)

"And of his fulness have all we received, and grace for grace. For the law was given by Moses, but grace and truth came by Jesus Christ" (John 1:16-17, KJV).