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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 3.2 × 1044 erg s-1, while the estimated total radiated energy is 1.3 × 1051 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, ΔV = 76 km s-1, 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. 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.