We have investigated the properties of vapor-deposited glasses prepared from short polymer chains using molecular dynamics simulations. Vapor-deposited polymer glasses are found to have higher density and higher kinetic stability than ordinary glasses prepared by gradual cooling of the corresponding equilibrium liquid. In contrast to results for binary Lennard-Jones glasses, the deposition rate is found to play an important role in the stability of polymer vapor-deposited glasses. Glasses deposited at the slowest deposition rate and at the optimal substrate temperature are found to correspond to the ordinary glasses that one could hypothetically prepare by cooling the liquid at rates that are 4-5 orders of magnitude slower than those accessible in the current simulations. For intermediate-length polymer chains, the resulting vapor-deposited glasses are found to be highly anisotropic. For short chains, however, the glasses are isotropic, showing that structural anisotropy is not a necessary condition for formation of stable glasses by physical vapor deposition.