A Born-Green-Yvon (BGY) integral equation is constructed for the end-to-end distribution function of an isolated polymer on a lattice. The polymer is modeled as a self-avoiding walk for which nonbonded sites interact via an attractive nearest-neighbor contact potential. The BGY equation is solved analytically using a Markov approximation for the required three-site distribution function and a delta-function pseudopotential to model the lattice contact potential. The resulting recursive algebraic equation is readily evaluated for a polymer on any Bravais lattice with equal length base vectors. Results are presented for the mean-square end-to-end separation as a function of chain length and contact energy for polymers on several two-, three-, and four-dimensional lattices. The variation of the scaling exponent 2 nu with contact energy is used to locate the theta energies for these lattices.