  Observations of elemental abundances in the Galaxy have repeatedly shown an
intrinsic scatter as a function of time and metallicity. The standard approach
to chemical evolution does not attempt to address this scatter in abundances
since only the mean evolution is followed. In this work the scatter is
addressed via a stochastic approach to solving chemical evolution models. Three
standard chemical evolution scenarios are studied using this stochastic
approach; a closed box model, an infall model, and an outflow model. These
models are solved for the solar neighborhood in a Monte Carlo fashion. The
evolutionary history of one particular region is determined randomly based on
the star formation rate and the initial mass function. Following the evolution
in an ensemble of such regions leads to the predicted spread in abundances
expected, based solely on different evolutionary histories of otherwise
identical regions. In this work 13 isotopes are followed including the light
elements, the CNO elements, a few $\alpha$-elements, and iron. It is found that
the predicted spread in abundances for a $10^5\Msun$ region is in good
agreement with observations for the $\alpha$-elements. For CN the agreement is
not as good perhaps indicating the need for more physics input for low mass
stellar evolution. Similarly for the light elements the predicted scatter is
quite small which is in contradiction to the observations of \He{3} in \hii\
regions. The models are tuned for the solar neighborhood so good agreement with
\hii\ regions is not expected. This has important implications for low mass
stellar evolution and on using chemical evolution to determine the primordial
light element abundances in order to test big-bang nucleosynthesis.
