  We report 2.1 mm observations of the Sunyaev-Zel'dovich (S-Z) effect; these
observations confirm our previous detection of a decrement in the Cosmic
Microwave Background intensity towards the cluster Abell 2163. The S-Z data are
analyzed using the relativistically correct expression for the Comptonization.
We begin by assuming the intracluster (IC) gas to be isothermal at the emission
weighted average temperature determined by a combined analysis of the ASCA and
GINGA X-ray satellite observations. Combining the X-ray and S-Z measurements,
we determine the Hubble constant to be H_0(q_0=0.5)= 60 +40/-23 km/s/Mpc, where
the uncertainty is dominated by the systematic difference in the ASCA and GINGA
determined IC gas temperatures. ASCA observations suggest the presence of a
significant thermal gradient in the IC gas. We determine $H_0$ as a function of
the assumed IC gas thermal structure. Using the ASCA determined thermal
structure and keeping the emission weighted average temperature the same as in
the isothermal case, we find H_0(q_0=0.5)= 78 +54/-28 km/s/Mpc. Including
additional uncertainties due to cluster asphericity, peculiar velocity, IC gas
clumping, and astrophysical confusion, we find H_0(q_0=0.5)= 78 +60/-40
km/s/Mpc.
