The 4D four-point scattering amplitude of massless scalars via a massive exchange is expressed in a basis of conformal primary particle wave functions. This celestial amplitude is expanded in a basis of 2D conformal partial waves on the unitary principal series, and then rewritten as a sum over 2D conformal blocks via contour deformation. The conformal blocks include intermediate exchanges of spinning light-ray states, as well as scalar states with positive integer conformal weights. The conformal block prefactors are found as expected to be quadratic in the celestial operator product expansion coefficients.