We present the optical and near-IR identification and spectroscopy of the host galaxy of gamma-ray burst GRB 980613. The burst was apparently associated with the optically (rest-frame UV) brightest component of an apparent system of at least five galaxies or galaxy fragments, at least two of which are at a redshift of z = 1.0969. The component we identify as the host galaxy shows a moderately high unobscured star formation rate, SFR ~ 5 M yr^-1, but a high SFR per unit mass, indicative of a starburst. The image components show a broad range of (R-K) colors, with two of them being very red, possibly due to dust. The overall morphology of the system can be naturally interpreted as a strong tidal interaction of two or more galaxies, at a redshift where such events were much more common than now. Given the well-established causal link between galaxy mergers and starbursts, we propose that this is a strong case for a GRB originating from a merger-induced starburst system. This supports the proposed link between GRBs and massive star formation.