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After large galaxies merge, their central supermassive black holes areexpected to form binary systems whose orbital motion generates a gravitationalwave background (GWB) at nanohertz frequencies. Searches for this backgroundutilize pulsar timing arrays, which perform long-term monitoring of millisecondpulsars (MSPs) at radio wavelengths. We use 12.5 years of Fermi Large AreaTelescope data to form a gamma-ray pulsar timing array. Results from 35 brightgamma-ray pulsars place a 95\% credible limit on the GWB characteristic strainof $1.0\times10^{-14}$ at 1 yr$^{-1}$, which scales as the observing time span$t_{\mathrm{obs}}^{-13/6}$. This direct measurement provides an independentprobe of the GWB while offering a check on radio noise models.

A Gamma-ray Pulsar Timing Array Constrains the Nanohertz Gravitational Wave Background