  We present near-infrared narrow- and broad-band imaging of the field of
GRB021004, performed with ISAAC on the UT1 of the ESO Very Large Telescope. The
narrow-band filters were chosen to match prominent emission lines at the
redshift of the absorption-line systems found against the early-time afterglow
of GRB021004: [OIII] at z=1.38 and Halpha at z=1.60, respectively. For the
z=1.38 system we find an emission-line source at an impact parameter of 16",
which is somewhat larger than the typical impact parameters of a sample of MgII
absorbers at redshifts around unity. Assuming that this tentative
redshift-identification is correct, the star formation rate of the galaxy is 13
+- 2 Msun/year. Our study reaches star-formation rate limits (5 sigma) of 5.7
Msun/year at z=1.38, and 7.7 Msun/year at z=1.60. These limits correspond to a
depth of roughly 0.13 L*. Any galaxy counterpart of the absorbers nearer to the
line of sight either has to be fainter than this limit or not be an
emission-line source.
