We report the detection of the Sunyaev-Zel'dovich effect in the Coma c
luster of galaxies with the 5.5 m telescope at the Owens Valley Radio
Observatory. The measured decrement of the temperature of the cosmic m
icrowave background is Delta T-0,T-obs,obs -270 +/- 29 mu K After corr
ecting for the effect of discrete radio sources and applying current m
odels for the X-ray atmosphere of the cluster, we calculate the peak o
f the effect to be Delta T-0(0) = -505 +/- 92 mu K. Using the same X-r
ay models, and assuming spherical symmetry for the gas atmosphere, we
derive a Hubble constant of H-0= 71(-25)(+30) km s(-1) Mpc(-1). This i
s the first detection of the Sunyaev-Zel'dovich effect in a nearby clu
ster of galaxies.