We present panchromatic resolved stellar photometry for 22 million stars in the Local Group dwarf spiral Triangulum (M33), derived from Hubble Space Telescope observations with the Advanced Camera for Surveys in the optical (F475W, F814W), and the Wide Field Camera 3 in the near-ultraviolet (F275W, F336W) and near-infrared (F110W, F160W) bands. The large, contiguous survey area covers ~14kpc^2^ and extends to 3.5kpc (14', or 1.5-2 scale lengths) from the center of M33. The PHATTER observing strategy and photometry technique closely mimics that of Panchromatic Hubble Andromeda Treasury, but with updated photometry techniques that take full advantage of all overlapping pointings (aligned to within <5-10mas) and improved treatment of spatially varying point-spread functions. The photometry reaches a completeness-limited depth of F475W~28.5 in the lowest surface density regions observed in M33 and F475W~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.