  I calculate the contribution of Bremsstrahlung emission from Lyman-alpha
absorption clouds to the brightness of the microwave sky. The calculation is
based only on the assumption that the clouds below the Lyman-limit are in
photoionization equilibrium with a UV background radiation, and avoids any
uncertainty about the clumpiness of the gas. I predict a minimum fluctuation
amplitude in the Rayleigh-Jeans regime of DeltaT/T =
10^{-5.5+-0.4}*J_21*(L/5cm)^2, which varies over characteristic angular scales
of 1-100'', where L is the observed wavelength and J_21 is a weighted redshift
average of the UV background intensity at the Lyman-limit in units of 10^{-21}
erg cm^{-2} s^{-1} Hz^{-1} sr^{-1}. Detection of this signal can be used to map
the intergalactic hydrogen distribution and to calibrate the UV background at
high redshifts. Existing VLA observations constrain J_21<10^{1.3+-0.4}, unless
some of the extended flat-spectrum sources which were detected are Lyman-alpha
absorption systems.
