We present deep HST/STIS and ground-based photometry of the host galaxy of the gamma-ray burst GRB 980703 taken 17, 551, 710, and 716 days after the burst. We find that the host is a blue, slightly over-luminous galaxy with V_gal = 23.00 +/- 0.10, (V-R)_gal = 0.43 +/- 0.13, and a centre that is approximately 0.2 mag bluer than the outer regions of the galaxy. The galaxy has a star-formation rate of 8-13 M_sun/yr, assuming no extinction in the host. We find that the galaxy is best fit by a Sersic R^(1/n) profile with n ~= 1.0 and a half-light radius of 0.13 arcsec (= 0.72/h_100 proper kpc). This corresponds to an exponential disk with a scale radius of 0.22 arcsec (= 1.21/h_100 proper kpc). Subtracting a fit with elliptical isophotes leaves large residuals, which suggests that the host galaxy has a somewhat irregular morphology, but we are unable to connect the location of GRB 980703 with any special features in the host. The host galaxy appears to be a typical example of a compact star forming galaxy similar to those found in the Hubble Deep Field North. The R-band light curve of the optical afterglow associated with this gamma-ray burst is consistent with a single power-law decay having a slope of alpha = -1.37 +/- 0.14. Due to the bright underlying host galaxy the late time properties of the light-curve are very poorly constrained. The decay of the optical light curve is consistent with a contribution from an underlying Type Ic supernova like SN1998bw, or a dust echo, but such contributions cannot be securely established.
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