  Baryon-density perturbations of large amplitude may exist if they are
compensated by dark-matter perturbations so that the total density remains
unchanged. Big-bang nucleosynthesis and galaxy clusters allow the amplitudes of
these compensated isocurvature perturbations (CIPs) to be as large as
$\sim10%$. CIPs will modulate the power spectrum of cosmic microwave background
(CMB) fluctuations---those due to the usual adiabatic perturbations---as a
function of position on the sky. This leads to correlations between different
spherical-harmonic coefficients of the temperature/polarization map, and it
induces B modes in the CMB polarization. Here, the magnitude of these effects
is calculated and techniques to measure them are introduced. While a CIP of
this amplitude can be probed on the largest scales with WMAP, forthcoming CMB
experiments should improve the sensitivity to CIPs by at least an order of
magnitude.
