  The Lyman-alpha absorption systems observed in the spectra of QSOs are likely
to possess bulk peculiar velocities. The free electrons in these systems
scatter the microwave background and distort its spectrum through the kinematic
Sunyaev-Zel'dovich effect. I calculate the temperature fluctuations of the
microwave sky due to variations in the number of Lyman-alpha systems along
different lines-of-sight throughout the universe. The known population of
absorbers out to z=5 introduces anisotropies on angular scales <1' with an rms
amplitude of order (DeltaT/T)= 10^{-6}*(Omega_Lya/0.05)*(v/400km/s), where
Omega_Lya is the cosmological density parameter of ionized gas in Lyman-alpha
absorption systems, and v is the rms line-of-sight peculiar velocity of these
systems at z=3. Detection of this signal will provide valuable information
about the cosmic velocity field and the gas content of Lyman-alpha absorption
systems at high redshifts.
