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An exact field theory is presented to describe a system of self-avoiding lattice polymer chains with arbitrary regularly branched architecture. Equivalently, the chains can be viewed as linear and as composed of structural units (monomers) having a chosen shape and size and therefore each occupying more than one lattice site. The mean field approximation coincides with Flory’s theory, and it does not distinguish among chain geometries. However, we develop a systematic expansion for corrections to mean field approximation in powers of z−1 where z is the lattice coordination number. The entropy per site, the pressure and the chain insertion probability are computed for various chain architectures to O(z−2). At equal lattice site coverages per chain and total polymer volume fraction, the more compact the polymer chain geometry the higher is the insertion probability.

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