After large galaxies merge, their central supermassive black holes are expected to form binary systems. Their orbital motion should generate a gravitational wave background (GWB) at nanohertz frequencies. Searches for this background use pulsar timing arrays, which perform long-term monitoring of millisecond pulsars at radio wavelengths. We used 12.5 years of Fermi Large Area Telescope data to form a gamma-ray pulsar timing array. Results from 35 bright gamma-ray pulsars place a 95% credible limit on the GWB characteristic strain of 1.0 × 10-14 at a frequency of 1 year-1. The sensitivity is expected to scale with tobs, the observing time span, as [Formula: see text]. This direct measurement provides an independent probe of the GWB while offering a check on radio noise models.