We report on X-ray, optical and infrared follow-up observations of GRB 980703. We detect a previously unknown X-ray source in the GRB error box; assuming a power law decline we find for its decay index alpha < -0.91 (3-sigma). We invoke host galaxy extinction to match the observed spectral slope with the slope expected from `fireball' models. We find no evidence for a spectral break in the infrared to X-ray spectral range on 1998 July 4.4, and determine a lower limit of the cooling break frequency: nu_c > 1.3 x 10^{17} Hz. For this epoch we obtain an extinction of A_V = 1.50 +/- 0.11. From the X-ray data we estimate the optical extinction to be A_V = 20.2 +12.3 -7.3, inconsistent with the former value. Our optical spectra confirm the redshift of z = 0.966 found by Djorgovski et al. (1998). We compare the afterglow of GRB 980703 with that of GRB 970508 and find that the fraction of the energy in the magnetic field, epsilon_B < 6x10^{-5}, is much lower in the case of GRB 980703, which is a consequence of the high frequency of the cooling break.

Accepted for publication in Part 1 of The Astrophysical Journal