  We present ultraviolet through near-infrared photometry and spectroscopy of
the host galaxies of all superluminous supernovae (SLSNe) discovered by the
Palomar Transient Factory prior to 2013, and derive measurements of their
luminosities, star-formation rates, stellar masses, and gas-phase
metallicities. We find that Type I (hydrogen-poor) SLSNe are found almost
exclusively in low-mass (M < 2x10^9 M_sun) and metal-poor (12+log[O/H] < 8.4)
galaxies. We compare the mass and metallicity distributions of our sample to
nearby galaxy catalogs in detail and conclude that the rate of SLSNe-I as a
fraction of all SNe is heavily suppressed in galaxies with metallicities >0.5
Z_sun. Extremely low metallicities are not required, and indeed provide no
further increase in the relative SLSN rate. Several SLSN-I hosts are undergoing
vigorous starbursts, but this may simply be a side effect of metallicity
dependence: dwarf galaxies tend to have bursty star-formation histories.
Type-II (hydrogen-rich) SLSNe are found over the entire range of galaxy masses
and metallicities, and their integrated properties do not suggest a strong
preference for (or against) low-mass/low-metallicity galaxies. Two hosts
exhibit unusual properties: PTF 10uhf is a Type I SLSN in a massive, luminous
infrared galaxy at redshift z=0.29, while PTF 10tpz is a Type II SLSN located
in the nucleus of an early-type host at z=0.04.
