  We present panchromatic resolved stellar photometry for 22 million stars in
the Local Group dwarf spiral Triangulum (M33), derived from Hubble Space
Telescope (HST) observations with the Advanced Camera for Surveys (ACS) in the
optical (F475W, F814W), and the Wide Field Camera 3 (WFC3) in the near
ultraviolet (F275W, F336W) and near-infrared (F110W, F160W) bands. The large,
contiguous survey area covers $\sim$14 square kpc and extends to 3.5 kpc (14
arcmin, or 1.5-2 scale lengths) from the center of M33. The PHATTER observing
strategy and photometry technique closely mimic those of the Panchromatic
Hubble Andromeda Treasury (PHAT), but with updated photometry techniques that
take full advantage of all overlapping pointings (aligned to within $<$5-10
milliarcseconds) and improved treatment of spatially-varying point spread
functions. The photometry reaches a completeness-limited depth of
F475W$\sim$28.5 in the lowest surface density regions observed in M33 and
F475W$\sim$26.5 in the most crowded regions found near the center of M33. We
find the young populations trace several relatively tight arms, while the old
populations show a clear, looser two-armed structure. We present extensive
analysis of the data quality including artificial star tests to quantify
completeness, photometric uncertainties, and flux biases. This stellar catalog
is the largest ever produced for M33, and is publicly available for download by
the community.
