Even-order PN theory has historically been viewed as a questionable approximation to transport theory. The main reason is that one obtains an odd number of unknowns and equations; this causes an ambiguity in the prescription of boundary conditions. We derive the one-group planar-geometry P2 equations and associated boundary conditions using a simple, physically motivated variational principle. We also present numerical results comparing P2, P1, and SN calculations. These results demonstrate that for most problems, the P2 equations with variational boundary conditions are considerably more accurate than the P1 equations with either the Marshak or the Federighi-Pomraning boundary conditions (both of which have also been derived variationally). Moreover, because the P2 and P1 equations can be written in diffusion form, the discretized P2 equations require nearly the same computational effort to solve as the discretized P1 equations. Our variational method can easily be extended to higher even-order PN approximations.