Abstract 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 BBHs, with m ₁ ≳ 45 M _⊙, are only found at the highest redshifts, z ≳ 0.4. We ask whether the absence of high-mass observations at low redshift indicates that the mass distribution evolves: the biggest BBHs only merge at high redshift, and cease merging at low redshift. 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 at z < 0.4 to at z > 0.4. Alternatively, if the primary-mass spectrum has a break in the power law (Broken Power Law) at , rather than a sharp cutoff, the data are consistent with a nonevolving mass distribution. In this case, the overall rate of mergers, at all masses, increases with redshift. Future observations will distinguish between a sharp mass cutoff that evolves with redshift and a nonevolving 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.