  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 LSQ12gdj's 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.
