We study the evolution of the binary black hole (BBH) mass distribution across cosmic time. The second gravitational-wave transient catalog (GWTC-2) from LIGO/Virgo contains BBH events out to redshifts z ∼ 1, with component masses in the range ∼ 5-80 M . In this catalog, the biggest black holes, with m 1 45 M , are only found at the highest redshifts, z 0.4. We ask whether the absence of high-mass BBH observations at low redshift indicates that the astrophysical BBH mass distribution evolves: the biggest BBHs only merge at high redshift, and cease merging at low redshift. Alternatively, this feature might be explained by gravitational-wave selection effects. Modeling the BBH primary mass spectrum as a power law with a sharp maximum mass cutoff (Truncated model), we find that the cutoff increases with redshift (> 99.9% credibility). An abrupt cutoff in the mass spectrum is expected from (pulsational) pair instability supernova simulations; however, GWTC-2 is only consistent with a Truncated mass model if the location of the cutoff increases from 45 +13 −5 M at z < 0.4 to 80 +16−13 M at z > 0.4. Alternatively, if the primary mass spectrum has a break in the power law (Broken Power Law ) at 38 +15 −8 M , rather than a sharp cutoff, the data are consistent with a non-evolving mass distribution. In this case the overall rate of mergers, at all masses, increases with increasing redshift. Future observations will confidently distinguish between a sharp maximum mass cutoff that evolves with redshift and a non-evolving mass distribution with a gradual taper, such as a Broken Power Law. After ∼ 100 BBH merger observations, a continued absence of high-mass, low-redshift events would provide a clear signature that the mass distribution evolves with redshift.