Objection 1. It would seem that a slave cannot marry without his master's consent. For no one can give a person that which is another's without the latter's consent. Now a slave is his master's chattel. Therefore he cannot give his wife power over his body by marrying without his master's consent.
Objection 2. Further, a slave is bound to obey his master. But his master may command him not to consent to marry. Therefore he cannot marry without his consent.
Objection 3. Further, after marriage, a slave is bound even by a precept of the Divine law to pay the debt to his wife. But at the time that his wife asks for the debt his master may demand of him a service which he will be unable to perform if he wish to occupy himself in carnal intercourse. Therefore if a slave can marry without his master's consent, the latter would be deprived of a service due to him without any fault of his; and this ought not to be.
Objection 4. Further, a master may sell his slave into a foreign country, where the latter's wife is unable to follow him, through either bodily weakness, or imminent danger to her faith; for instance if he be sold to unbelievers, or if her master be unwilling, supposing her to be a bondswoman; and thus the marriage will be dissolved, which is unfitting. Therefore a slave cannot marry without his master's consent.
Objection 5. Further, the burden under which a man binds himself to the Divine service is more advantageous than that whereby a man subjects himself to his wife. But a slave cannot enter religion or receive orders without his master's consent. Much less therefore can he be married without his consent.
On the contrary, "In Christ Jesus... there is neither bond nor free" (Galatians 3:26-28). Therefore both freeman and bondsman enjoy the same liberty to marry in the faith of Christ Jesus.
Further, slavery is of positive law; whereas marriage is of natural and Divine law. Since then positive law is not prejudicial to the natural or the Divine law, it would seem that a slave can marry without his master's consent.
I answer that, As stated above (1, ad 3), the positive law arises out of the natural law, and consequently slavery, which is of positive law, cannot be prejudicious to those things that are of natural law. Now just as nature seeks the preservation of the individual, so does it seek the preservation of the species by means of procreation; wherefore even as a slave is not so subject to his master as not to be at liberty to eat, sleep, and do such things as pertain to the needs of his body, and without which nature cannot be preserved, so he is not subject to him to the extent of being unable to marry freely, even without his master's knowledge or consent.
Reply to Objection 1. A slave is his master's chattel in matters superadded to nature, but in natural things all are equal. Wherefore, in things pertaining to natural acts, a slave can by marrying give another person power over his body without his master's consent.
Reply to Objection 2. A slave is bound to obey his master in those things which his master can command lawfully; and just as his master cannot lawfully command him not to eat or sleep, so neither can he lawfully command him to refrain from marrying. For it is the concern of the lawgiver how each one uses his own, and consequently if the master command his slave not to marry, the slave is not bound to obey his master.
Reply to Objection 3. If a slave has married with his master's consent, he should omit the service commanded by his master and pay the debt to his wife; because the master, by consenting to his slave's marriage, implicitly consented to all that marriage requires. If, however, the marriage was contracted without the master's knowledge or consent, he is not bound to pay the debt, but in preference to obey his master, if the two things are incompatible. Nevertheless in such matters there are many particulars to be considered, as in all human acts, namely the danger to which his wife's chastity is exposed, and the obstacle which the payment of the debt places in the way of the service commanded, and other like considerations, all of which being duly weighed it will be possible to judge which of the two in preference the slave is bound to obey, his master or his wife.
Reply to Objection 4. In such a case it is said that the master should be compelled not to sell the slave in such a way as to increase the weight of the marriage burden, especially since he is able to obtain anywhere a just price for his slave.
Reply to Objection 5. By entering religion or receiving orders a man is bound to the Divine service for all time; whereas a husband is bound to pay the debt to his wife not always, but at a fitting time; hence the comparison fails. Moreover, he who enters religion or receives orders binds himself to works that are superadded to natural works, and in which his master has power over him, but not in natural works to which a man binds himself by marriage. Hence he cannot vow continence without his master's consent.
Source: Summa Theologica (New Advent)