We consider the Seebeck coefficient in LaCrO3 and related transition-metal-oxide perovskites using a model for electronic conduction based on the electronic structure of the 3d orbitals of the B-site transition-metal cations. Relations for the Seebeck coefficient are presented for those perovskite systems in which electronic conduction is through the t2g states of the B-site transition-metal cations. High- and low-temperature limits for the Seebeck coefficient are identified for the cases of both strong and weak magnetic coupling between electron spins. In these high- and low-temperature limits, the Seebeck coefficient is determined as a function of carrier concentration. Results are applied to an analysis of experimental data for the (La,Sr)CrO3