We present the Pan-STARRS1 discovery and light curves, and follow-up MMT and Gemini spectroscopy of an ultra-luminous supernova (ULSN; dubbed PS1-11bam) at a redshift of z=1.566 with a peak brightness of M_UV=-22.3 mag. PS1-11bam is one of the highest redshift spectroscopically-confirmed SNe known to date. The spectrum is characterized by broad absorption features typical of previous ULSNe (e.g., CII, SiIII), and by strong and narrow MgII and FeII absorption lines from the interstellar medium (ISM) of the host galaxy, confirmed by an [OII]3727 emission line at the same redshift. The equivalent widths of the FeII2600 and MgII2803 lines are in the top quartile of the quasar intervening absorption system distribution, but are weaker than those of gamma-ray burst intrinsic absorbers (i.e., GRB host galaxies). We also detect the host galaxy in pre-explosion Pan-STARRS1 data and find that its UV spectral energy distribution is best fit with a young stellar population age of tau~15-45 Myr and a stellar mass of M \sim (1.1-2.6)x10^9 M_sun (for Z=0.05-1 Z_sun). The star formation rate inferred from the UV continuum and [OII]3727 emission line is ~10 M_sun/yr, higher than in any previous ULSN host. PS1-11bam provides the first direct demonstration that ULSNe can serve as probes of the interstellar medium in distant galaxies. At the present, the depth and red sensitivity of PS1 are uniquely suited to finding such events at cosmologically interesting redshifts (z~1-2); the future combination of LSST and 30-m class telescopes promises to extend this technique to z~4.