Fast Radio Bursts (FRBs) are millisecond-long bursts of GHz-frequency emission that appear to be of cosmological origin. The high all-sky rate of FRBs, R~2100 per day, and estimated energy outputs of E_GHz~10^41 erg combine with limits on repetition for most (but not all!) FRBs to raise substantial challenges for models. I will present results of our search for gamma-ray counterparts to FRBs, which resulted in discovery of the first non-radio counterpart to any FRB, a 3.2-sigma gamma-ray transient detected by the Swift BAT in association with FRB 131104. The transient has duration T_90 >~ 100 s and fluence S_gamma ~ 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 bursts gamma-ray energy output is E_gamma ~ 5 x 10^51 erg. I will present the results of follow-up campaigns carried out for this burst, and discuss the implications for FRB source models. I will also discuss ongoing work at the Astrophysical Multimessenger Observatory Network (AMON) to generate real-time neutrino + gamma-ray alerts from coincidence analysis of data from high-energy neutrino and gamma-ray observatories.