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We report on our serendipitous pre-discovery detection and follow-up observations of the broad-lined Type Ic supernova (SN Ic) 2010ay at z = 0.067 imaged by the Pan-STARRS1 3π survey just ∼4 days after explosion. The supernova (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 x 10³ 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 ⁵⁶Ni, M_Ni= 0.9 M_☉. Applying scaling relations to the light curve, we estimate a total ejecta mass, M_ej~ 4.7 M_☉, and total kinetic energy, E_K~ 11x10⁵¹ erg. The ratio of M_Ni to M_ejis ∼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) SNe Ic. We constrain any gamma-ray emission with E_γ ≲ 6x10⁴⁸ erg (25-150 keV), and our deep radio follow-up observations with the Expanded Very Large Array rule out relativistic ejecta with energy E ≳ 10⁴⁸ erg. We therefore rule out the association of a relativistic outflow like those that accompanied SN 1998bw and traditional long-duration gamma-ray bursts (GRBs), but we place less-stringent constraints on a weak afterglow like that seen from XRF 060218. If this SN did not harbor a GRB, these observations challenge the importance of progenitor metallicity for the production of relativistic ejecta and suggest that other parameters also play a key role.