Since the Second Vatican Ecumenical Council, the Church permits the concelebration of the Holy Mass under certain conditions. For instance, priests are permitted to concelebrate with the Bishop on the occasion of the Chrism Mass for which the priests of the Diocese are urged to be present as a sign of their communion with the Bishop in the priestly care of all the faithful.

Before the post-conciliar reforms, concelebration was permitted only in Ordination Masses of a Priest or Bishop, and the concelebration was limited to those ordained a priest or Bishop during the Holy Mass. For example, when an Ordination Mass of a Priest is celebrated in the Extraordinary Form, it is concelebrated by the principal Bishop who is ordaining and those whom he has just ordained. 

As the legislation implementing the wider permission makes clear, the norm is the individual offering of the Holy Mass individually by the priest. Concelebration is permitted only on certain occasions, as long as it does not in any way violate the good of the faithful, for instance, who would be denied the possibility of assisting at the Holy Mass. Each concelebrating priest is permitted to accept an offering for the concelebrated Holy Mass. He is obliged to apply the intention to the concelebrated Holy Mass, according to the norms of the Church’s discipline. The fact that, in a concelebrated Holy Mass, many intentions are applied – as is opposed to the discipline regarding the individual celebration of the Holy Mass in which only one intention can be applied – does not mean that many Holy Masses are being celebrated simultaneously or in the same action. A concelebrated Holy Mass is only ONE Holy Mass offered by the concelebrating priest or priests together with the principal celebrant.

When the conditions permitting concelebration are verified, it remains the decision of the individual priest whether to concelebrate or not. A priest is never obliged to concelebrate. (For Advanced Course 20-13 & 20-114.)
(See Sacrosanctum Concilium nos. 57-58; 1983 Code of Canon Law can. 902; General Instruction of the Roman Missal nos. 199-251, from the Third Typical Edition)