New stellar models which track the production and destruction of {sup 3}He (and D) have been evolved for a range of stellar masses (0.65{le}{ital M}/{ital M}{sub {circle_dot}}{le}100), metallicities (0.01{le}{ital Z}/{ital Z}{sub {circle_dot}}{le}1), and initial (main-sequence) {sup 3}He mass fractions (10{sup {minus}5}{le}{ital X}{sub 3,MS}{le}10{sup {minus}3}). Armed with the {sup 3}He yields from these stellar models we have followed the evolution of D and {sup 3}He using a variety of chemical evolution models with and without infall of primordial or processed material. Production of new {sup 3}He by the lower mass stars overwhelms any reasonable primordial contributions and leads to predicted abundances in the presolar nebula and/or the present interstellar medium in excess of the observationally inferred values. This result, which obtains even for zero primordial D and {sup 3}He, and was anticipated by Rood, Steigman, & Tinsley is insensitive to the choice of chemical evolution model; it is driven by the large {sup 3}He yields from low-mass stars. In an attempt to ameliorate this problem we have considered a number of nonstandard models in which the yields from low-mass stars have been modified. Although several of these nonstandard models may be consistent with the {sup 3}He data, they may be inconsistentmore » with observations of {sup 12}C/{sup 13}C, {sup 18}O, and, most seriously the super-{sup 3}He rich planetary nebulae. Even using the most extreme of these nonstandard models we obtain a generous upper bound to pregalactic {sup 3}He:{ital X}{sub 3{ital P}}{le}3.2{times}10{sup {minus}5} which, nonetheless, leads to a stringent lower bound to the universal density of nucleons. {copyright} {ital 1996 The American Astronomical Society.}« less