Summa Theologica, by St. Thomas Aquinas, [1947], at sacred-texts.com
We must now consider the minister of this sacrament: under which head there are three points of inquiry:
(1) Whether a layman can confer this sacrament?
(2) Whether a deacon can?
(3) Whether none but a bishop can confer it?
Objection 1: It would seem that even a layman can confer this sacrament. For this sacrament derives its efficacy from prayer, as James declares (James 5:15). But a layman's prayer is sometimes as acceptable to God as a priest's. Therefore he can confer this sacrament.
Objection 2: Further, we read of certain fathers in Egypt that they sent the oil to the sick, and that these were healed. It is also related of the Blessed Genevieve that she anointed the sick with oil. Therefore this sacrament can be conferred even by lay people.
On the contrary, Remission of sins is given in this sacrament. But laymen have not the power to forgive sins. Therefore, etc.
I answer that, According to Dionysius (Eccl. Hier. v) there are some who exercise hierarchical actions, and some who are recipients only. Hence laymen are officially incompetent to dispense any sacrament: and that they can baptize in cases of necessity, is due to the Divine dispensation, in order that no one may be deprived of spiritual regeneration.
Reply to Objection 1: This prayer is not said by the priest in his own person, for since sometimes he is in sin, he would not in that case be heard. But it is said in the person of the whole Church, in whose person he can pray as a public official, whereas a layman cannot, for he is a private individual.
Reply to Objection 2: These unctions were not sacramental. It was due to the devotion of the recipients of the unction, and to the merits of those who anointed them that they procured the effects of bodily health, through the "grace of healing" (1 Cor. 12:9) but not through sacramental grace.
Objection 1: It would seem that deacons can confer this sacrament. For, according to Dionysius (Eccl. Hier. v) "deacons have the power to cleanse." Now this sacrament was instituted precisely to cleanse from sickness of the mind and body. Therefore deacons also can confer it.
Objection 2: Further, Baptism is a more excellent sacrament than the one of which we are speaking. But deacons can baptize, as instanced by the Blessed Laurence. Therefore they can confer this sacrament also.
On the contrary, It is written (James 5:14): "Let him bring in the priests of the Church."
I answer that, A deacon has the power to cleanse but not to enlighten. Hence, since enlightenment is an effect of grace, no sacrament whereby grace is conferred can be given by a deacon in virtue of his office: and so he cannot confer this sacrament, since grace is bestowed therein.
Reply to Objection 1: This sacrament cleanses by enlightening through the bestowal of grace: wherefore a deacon is not competent to confer it.
Reply to Objection 2: This is not a necessary sacrament, as Baptism is. Hence its bestowal is not committed to all in cases of necessity, but only to those who are competent to do so in virtue of their office. Nor are deacons competent to baptize in virtue of their office.
Objection 1: It would seem that none but a bishop can confer this sacrament. For this sacrament consists in an anointing, just as Confirmation does. Now none but a bishop can confirm. Therefore only a bishop can confer this sacrament.
Objection 2: Further, he who cannot do what is less cannot do what is greater. Now the use of consecrated matter surpasses the act of consecrating the matter, since the former is the end of the latter. Therefore since a priest cannot consecrate the matter, neither can he use the matter after it has been consecrated.
On the contrary, The minister of this sacrament has to be brought in to the recipient, as is clear from James 5:14. Now a bishop cannot go to all the sick people of his diocese. Therefore the bishop is not the only one who can confer this sacrament.
I answer that, According to Dionysius (Eccl. Hier. v), the office of perfecting belongs to a bishop, just as it belongs to a priest to enlighten. Wherefore those sacraments are reserved to a bishop's dispensation, which place the recipient in a state of perfection above others. But this is not the case with this sacrament, for it is given to all. Consequently it can be given by ordinary priests.
Reply to Objection 1: Confirmation imprints a character, whereby man is placed in a state of perfection, as stated above (TP, Q[63], AA[1], 2,6). But this does not take place in this sacrament; hence there is no comparison.
Reply to Objection 2: Although the use of consecrated matter is of more importance than the consecration of the matter, from the point of view of the final cause; nevertheless, from the point of view of efficient cause, the consecration of the matter is the more important, since the use of the matter is dependent thereon, as on its active cause: hence the consecration of the matter demands a higher power than the use of the matter does.