Question: Can a priest (not a bishop) give the Sacrament of Confirmation?
Answer: In the earliest days of the Church, bishops presided more or less directly over the small number of Christians in those cities that had received the Faith. Even when assisted by deacons and priests, the bishop was able to remain in personal contact with the members of his flock. As most people were baptized as adults after a period of instruction, the bishop baptized all of the converts in his charge, usually on one of the three "baptismal feasts" of the Church year; Easter, Pentecost, and Epiphany. (Even in modern times, Easter and Pentecost are observed with a vigil in which the Baptismal Water is blessed, and Epiphany with a vigil blessing of Holy Water.) Under these conditions, it was the norm for the bishop immediately to confirm the newly baptized.
When Christianity became legal in the fourth century Roman Empire, it began to grow at a rate that made regular personal contact with one's bishop unlikely or impossible for most people. The same legalization made the Baptism of children more common. As families began to have a history of belonging to the Church, their infants began to be baptized with the now reasonable expectation that they would grow up practicing the Faith of their parents. In many of the Eastern Churches, Catholics dealt with this turn of events by having the priest who baptized their children confer the Sacrament of Confirmation immediately thereafter. In the West, the two Sacraments were generally separated, with a simple priest pouring the waters of Baptism, and a wait for the visit of the bishop to complete the process with an anointing of Chrism and the laying on of his hand.
In either case -- Eastern or Western -- Confirmation is understood as the Sacrament by which the Holy Ghost is received in a special way so as to make the baptized Christian firm in his Faith; "a soldier of Christ," as we usually say. It was only with Luther and the rise of Protestantism that his followers began to understand Confirmation as a reaffirmation of the promises made for them when baptized as infants.
Yet, even in the West, the Church has always been aware of the importance of the Sacrament of Confirmation, and taken steps to provide it for those whose wait for the bishop may be unreasonable or interminable. In missionary territories priests may be delegated to confirm, parish priests may confirm their parishioners in danger of death, prefects apostolic and prelates nullius (priest-administrators of a mission territory or of a small but established Catholic territory) may confirm within their territory, monastic Abbots may confirm their subjects, and Cardinals may confirm anywhere.1 The New Order allows the local bishop to grant faculties to confirm to any of his priests, either together with him, or when they have been instrumental in the instruction of a convert.2
The generally accepted principle governing Confirmation by simple priests is that they have the power to do so by virtue of their ordination, and may be allowed to do so by virtue of specific law (e.g. the pastor confirming his dying parishioner) or delegation (e.g. the missionary given authority to confirm without regard to specific parish or diocesan structures). There are strong penalties levied against priests who confirm without appropriate authorization.3
The Roman Ritual contains a section for the priestly administration of the Sacrament that is essentially identical to that given in the Pontifical. It cautions priests to remind those in attendance that the bishop is the ordinary minister of Confirmation and to explain that the priest is acting in accordance with an extraordinary delegation of authority. Heretics and schismatics are to be excluded from the ceremony -- probably to eliminate the use of their testimony to claim inconsistency on the part of the Church.4
1. Rituale Romanum, (Ratisbone: 1935) Appendix, pp. 456-464; Donald Attwater, A Catholic Dictionary, s.v. "Confirmation, The Sacrament of."
2. The Rites of the Catholic Church, (Collegeville: Liturgical Press, 1990), p. 481.
3. Canon 2365.
4. Rituale Romanum, ibid.