We report on our serendipitous pre-discovery detection and detailed follow-up of the broad-lined Type Ic supernova (SN) 2010ay at z = 0.067 imaged by the Pan-STARRS1 3pi survey just ~4 days after explosion. The SN had a peak luminosity, M_R ~ -20.2 mag, significantly more luminous than known GRB-SNe and one of the most luminous SNe Ib/c ever discovered. The absorption velocity of SN 2010ay is v_Si ~ 19,000 km/s at ~40 days after explosion, 2-5 times higher than other broad-lined SNe and similar to the GRB-SN 2010bh at comparable epochs. Moreover, the velocity declines ~2 times slower than other SNe Ic-BL and GRB-SNe. Assuming that the optical emission is powered by radioactive decay, the peak magnitude implies the synthesis of an unusually large mass of 56 Ni, M_Ni = 0.9 M_solar. Modeling of the light-curve points to a total ejecta mass, M_ej ~ 4.7 M_sol, and total kinetic energy, E_K ~ 11x10^51 ergs. The ratio of M_Ni to M_ej is ~2 times as large for SN 2010ay as typical GRB-SNe and may suggest an additional energy reservoir. The metallicity (log(O/H)_PP04 + 12 = 8.19) of the explosion site within the host galaxy places SN 2010ay in the low-metallicity regime populated by GRB-SNe, and ~0.5(0.2) dex lower than that typically measured for the host environments of normal (broad-lined) Ic supernovae. We constrain any gamma-ray emission with E_gamma < 6x10^{48} erg (25-150 keV) and our deep radio follow-up observations with the Expanded Very Large Array rule out relativistic ejecta with energy, E > 10^48 erg. We therefore rule out the association of a relativistic outflow like those which accompanied SN 1998bw and traditional long-duration GRBs, but place less-stringent constraints on a weak afterglow like that seen from XRF 060218. These observations challenge the importance of progenitor metallicity for the production of a GRB, and suggest that other parameters also play a key role.