  We report our discovery in Swift satellite data of a transient gamma-ray
counterpart (3.2$\sigma$ confidence) to the fast radio burst FRB131104, the
first such counterpart to any FRB. The transient has duration $T_{90} \gtrsim
100$s and fluence $S_\gamma\approx 4\times 10^{-6}$ erg cm$^{-2}$, increasing
the energy budget for this event by more than a billion times; at the nominal
$z\approx 0.55$ redshift implied by its dispersion measure, the burst's
gamma-ray energy output is $E_\gamma \approx 5\times 10^{51}$ erg. The observed
radio to gamma-ray fluence ratio for FRB131104 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, $D\gtrsim 320$ 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.
