We report our discovery in Swift satellite data of a transient gamma-ray counterpart (3.2σ confidence) to the fast radio burst FRB 131104, the first such counterpart to any FRB. The transient has duration T 90 ∼ > 100 s and fluence S γ ≈ 4 × 10 −6 erg cm −2 , increasing the energy budget for this event by more than a billion times; at the nominal z ≈ 0.55 redshift implied by its dispersion measure, the burst's gamma-ray energy output is E γ ≈ 5 × 10 51 erg. The observed radio to gamma-ray fluence ratio for FRB 131104 is consistent with a lower limit we derive from Swift observations of another FRB, which is not detected in gamma-rays, and with an upper limit previously derived for the brightest gamma-ray flare from SGR 1806−20, which was not detected in the radio. X-ray, ultraviolet, and optical observations beginning two days after the FRB do not reveal any associated afterglow, supernova, or transient; Swift observations exclude association with the brightest 65% of Swift gamma-ray burst X-ray afterglows, while leaving the possibility of an associated supernova at much more than 10% the FRB's nominal distance, D ∼ > 320 Mpc, largely unconstrained. Transient high-luminosity gamma-ray emission arises most naturally in a relativistic outflow or shock breakout, as for example from magnetar flares, gamma-ray bursts, relativistic supernovae, and some types of galactic nuclear activity. Our discovery thus bolsters the case for an extragalactic origin for some FRBs and suggests that future rapid-response observations might identify long-lived counterparts, resolving the nature of these mysterious phenomena and realizing their promise as probes of cosmology and fundamental physics.