We present imaging and spectroscopy of a hydrogen-poor superluminous supernova (SLSN) discovered by the intermediate Palomar Transient Factory, iPTF 13ajg. At a redshift of z=0.7403, derived from narrow absorption lines, iPTF 13ajg peaked at an absolute magnitude of M_u,AB_=-22.5, one of the most luminous supernovae to date. The observed bolometric peak luminosity of iPTF 13ajg is 3.2x10^44^ erg/s, while the estimated total radiated energy is 1.3x10^51^ erg. We detect narrow absorption lines of Mg I, Mg II, and Fe II, associated with the cold interstellar medium in the host galaxy, at two different epochs with X-shooter at the Very Large Telescope. From Voigt profile fitting, we derive the column densities log N(Mg I)=11.94+/-0.06, log N(Mg II)=14.7+/-0.3, and log N(Fe II)=14.25+/-0.10. These column densities, as well as the Mg I and Mg II equivalent widths of a sample of hydrogen-poor SLSNe taken from the literature, are at the low end of those derived for gamma-ray bursts (GRBs) whose progenitors are also thought to be massive stars. This suggests that the environments of hydrogen-poor SLSNe and GRBs are different. From the nondetection of Fe II fine-structure absorption lines, we derive a lower limit on the distance between the supernova and the narrow-line absorbing gas of 50 pc. The neutral gas responsible for the absorption in iPTF 13ajg exhibits a single narrow component with a low velocity width, {Delta}V=76 km/s, indicating a low-mass host galaxy. No host galaxy emission lines are detected, leading to an upper limit on the unobscured star formation rate (SFR) of SFR_[OII]_<0.07 M_{sun}_/yr. Late-time imaging shows the iPTF 13ajg host galaxy to be faint, with g_AB_~27.0 and R_AB_>=26.0 mag, corresponding to M_B,Vega_>~-17.7 mag.