  Energy injected into the Cosmic Microwave Background at redshifts z<10^6 will
distort its spectrum permanently. In this paper we discuss the distortion
caused by annihilations of relic particles. We use the observational bounds on
deviations from a Planck spectrum to constrain a combination of annihilation
cross section, mass, and abundance. For particles with (s-wave) annihilation
cross section, <\sigma|v|>=\sigma_0, the bound is
f[(\sigma_0/6e-27cm^3/s)(\Omega_{X\bar{X}}h^2)^2]/(m_X/MeV)<0.2, where m_X is
the particle mass, \Omega_{X\bar{X}} is the fraction of the critical density
the particle and its antiparticle contribute if they survive to the present
time, h=H_0/(100km/s/Mpc), H_0 is the Hubble constant, and f is the fraction of
the annihilation energy that interacts electromagnetically. We also compute the
less stringent limits for p-wave annihilation. We update other bounds on
residual annihilations and compare them to our CMB bound.
