We present photospheric-phase observations of LSQ12gdj, a slowly-declining, UV-bright Type Ia supernova. Classified well before maximum light, LSQ12gdj has extinction-corrected absolute magnitude $M_B = -19.8$, and pre-maximum spectroscopic evolution similar to SN 1991T and the super-Chandrasekhar-mass SN 2007if. We use ultraviolet photometry from Swift, ground-based optical photometry, and corrections from a near-infrared photometric template to construct the bolometric (1600-23800 AA) light curve out to 45 days past $B$-band maximum light. We estimate that LSQ12gdj produced $0.96 pm 0.07$ $M_odot$ of $^{56}$Ni, with an ejected mass near or slightly above the Chandrasekhar mass. As much as 27% of the flux at the earliest observed phases, and 17% at maximum light, is emitted bluewards of 3300 AA. The absence of excess luminosity at late times, the cutoff of the spectral energy distribution bluewards of 3000 AA, and the absence of narrow line emission and strong Na I D absorption all argue against a significant contribution from ongoing shock interaction. However, up to 10% of LSQ12gdjs luminosity near maximum light could be produced by the release of trapped radiation, including kinetic energy thermalized during a brief interaction with a compact, hydrogen-poor envelope (radius $< 10^{13}$ cm) shortly after explosion; such an envelope arises generically in double-degenerate merger scenarios.
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