Objection 1. It seems that vengeance is not a special and distinct virtue. For just as the good are rewarded for their good deeds, so are the wicked punished for their evil deeds. Now the rewarding of the good does not belong to a special virtue, but is an act of commutative justice. Therefore in the same way vengeance should not be accounted a special virtue.
Objection 2. Further, there is no need to appoint a special virtue for an act to which a man is sufficiently disposed by the other virtues. Now man is sufficiently disposed by the virtues of fortitude or zeal to avenge evil. Therefore vengeance should not be reckoned a special virtue.
Objection 3. Further, there is a special vice opposed to every special virtue. But seemingly no special vice is opposed to vengeance. Therefore it is not a special virtue.
On the contrary, Tully (De Invent. Rhet. ii) reckons it a part of justice.
I answer that, As the Philosopher states (Ethic. ii, 1), aptitude to virtue is in us by nature, but the complement of virtue is in us through habituation or some other cause. Hence it is evident that virtues perfect us so that we follow in due manner our natural inclinations, which belong to the natural right. Wherefore to every definite natural inclination there corresponds a special virtue. Now there is a special inclination of nature to remove harm, for which reason animals have the irascible power distinct from the concupiscible. Man resists harm by defending himself against wrongs, lest they be inflicted on him, or he avenges those which have already been inflicted on him, with the intention, not of harming, but of removing the harm done. And this belongs to vengeance, for Tully says (De Invent. Rhet. ii) that by "vengeance we resist force, or wrong, and in general whatever is obscure" ['Obscurum' Cicero wrote 'obfuturum' but the sense is the same as St. Thomas gives in the parenthesis] "(i.e. derogatory), either by self-defense or by avenging it." Therefore vengeance is a special virtue.
Reply to Objection 1. Just as repayment of a legal debt belongs to commutative justice, and as repayment of a moral debt, arising from the bestowal of a particular favor, belongs to the virtue of gratitude, so too the punishment of sins, so far as it is the concern of public justice, is an act of commutative justice; while so far as it is concerned in defending the rights of the individual by whom a wrong is resisted, it belongs to the virtue of revenge.
Reply to Objection 2. Fortitude disposes to vengeance by removing an obstacle thereto, namely, fear of an imminent danger. Zeal, as denoting the fervor of love, signifies the primary root of vengeance, in so far as a man avenges the wrong done to God and his neighbor, because charity makes him regard them as his own. Now every act of virtue proceeds from charity as its root, since, according to Gregory (Hom. xxvii in Ev.), "there are no green leaves on the bough of good works, unless charity be the root."
Reply to Objection 3. Two vices are opposed to vengeance: one by way of excess, namely, the sin of cruelty or brutality, which exceeds the measure in punishing: while the other is a vice by way of deficiency and consists in being remiss in punishing, wherefore it is written (Proverbs 13:24): "He that spareth the rod hateth his son." But the virtue of vengeance consists in observing the due measure of vengeance with regard to all the circumstances.
Source: Summa Theologica (New Advent)