  We investigate the spatial clustering properties of primordial black holes
(PBHs). With minimal assumptions, we show that PBHs created in the radiation
era are highly clustered. Using the peaks theory model of bias, we compute the
PBH two-point correlation function and power spectrum. For creation from an
initially adiabatic power spectrum of perturbations, the PBH power spectrum
contains both isocurvature and adiabatic components. The absence of observed
isocurvature fluctuations today constrains the mass range in which PBHs may
serve as dark matter. We briefly discuss other consequences of PBH clustering.
