We investigate the effect of helium enrichment on the evolution and nucleosynthesis of low-mass asymptotic giant branch (AGB) stars of 1.7 M ☉ and 2.36 M ☉ with a metallicity of Z = 0.0006 ([Fe/H] ≈–1.4). We calculate evolutionary sequences with the primordial helium abundance (Y = 0.24) and with helium-enriched compositions (Y = 0.30, 0.35, 0.40). For comparison, we calculate models of the same mass but at a lower metallicity Z = 0.0003 ([Fe/H] ≈–1.8) with Y = 0.24. Post-processing nucleosynthesis calculations are performed on each of the evolutionary sequences to determine the production of elements from hydrogen to bismuth. Elemental surface abundance predictions and stellar yields are presented for each model. The models with enriched helium have shorter main sequence and AGB lifetimes, and they enter the AGB with a more massive hydrogen-exhausted core than the primordial helium model. The main consequences are as follows: (1) low-mass AGB models with enhanced helium will evolve more than twice as fast, giving them the chance to contribute sooner to the chemical evolution of the forming globular clusters, and (2) the stellar yields will be strongly reduced relative to their primordial helium counterparts. An increase of ΔY = 0.10 at a given mass decreases the yields of carbon by up to ≈60% and of fluorine by up to 80%; it also decreases the yields of the s-process elements barium and lanthanum by ≈45%. While the yields of first s-process peak elements strontium, yttrium, and zirconium decrease by up to 50%, the yields of rubidium either do not change or increase.