  We analyze simulated maps of the Cosmology Large Angular Scale Surveyor
(CLASS) experiment and recover a nearly cosmic-variance limited estimate of the
reionization optical depth $\tau$. We use a power spectrum-based likelihood to
simultaneously clean foregrounds and estimate cosmological parameters in
multipole space. Using software specifically designed to constrain $\tau$, the
amplitude of scalar fluctuations $A_s$, and the tensor-to-scalar ratio $r$, we
demonstrate that the CLASS experiment will be able to estimate $\tau$ within a
factor of two of the full-sky cosmic variance limit allowed by cosmic microwave
background polarization measurements. Additionally, we discuss the role of
CLASS's $\tau$ constraint in conjunction with gravitational lensing of the CMB
on obtaining a $\gtrsim4\sigma$ measurement of the sum of the neutrino masses.
