Compensated isocurvature perturbations (CIPs) are modulations of the relative
baryon and dark matter density that leave the total matter density constant.
The best current constraints from the primary cosmic microwave background (CMB)
are consistent with CIPs some two orders of magnitude larger in amplitude than
adiabatic perturbations, suggesting that there may be a huge gap in our
knowledge of the early Universe. However, it was recently suggested by
Barreira~et.~al. that CIPs which are correlated with the primordial curvature
perturbation, as arises in some versions of the curvaton model, lead to a new
observable: scale dependent galaxy bias. Combining a galaxy survey with an
unbiased tracer of the density field facilitates a measurement of the amplitude
of correlated CIPs that is free from cosmic variance, the main limitation on
constraints from the primary CMB. Among the most promising tracers to use for
this purpose is the remote dipole field, reconstructed using the technique of
kinetic Sunyaev Zel'dovich (kSZ) tomography. In this paper, we evaluate the
detection significance on the amplitude of correlated CIPs possible with
next-generation CMB and galaxy surveys using kSZ tomography. Our analysis
includes all relativistic contributions to the observed galaxy number counts
and allows for both CIPs and primordial non-Gaussianity, which also gives rise
to a scale dependent galaxy bias. We find that kSZ tomography can probe CIPs of
comparable amplitude to the adiabatic fluctuations, representing an improvement
of over two orders of magnitude upon current constraints, and an order of
magnitude over what will be possible using future CMB or galaxy surveys alone.