GRB 970828 was the first well-localized γ-ray burst (GRB) X-ray afterglow for which no optical afterglow was found despite a prompt, deep search down to R$_lim$åisebox-0.5ex 24.5 mag. We report the discovery of a short-lived radio flare within the X-ray localization error circle of this burst. Such radio flares are seen in about 25% of GRB afterglows, and their origin is not well understood. The precise radio position enabled us to identify the likely host galaxy of this burst and to measure its redshift, z=0.9578. The host appears to be an interacting/merging system. Under the assumption that the X-ray afterglow is mainly due to synchrotron mechanism, we infer the optical afterglow flux. The observed upper limits to the optical flux are easily explained by invoking an intervening dusty cloud within the host galaxy. These observations support the idea that GRBs with no detectable optical afterglows, or ``dark GRBs,’’ can be due to dust extinction within the host galaxies. The census of dark GRBs can then be used to constrain the fraction of the obscured star formation in the universe. We argue that the existing data already indicate that the obscured star formation rate is no more than one-half of that seen at UV and optical wavelengths. Partially based on the observations obtained at the W. M. Keck Observatory, which is operated by the California Association for Research in Astronomy, a scientific partnership among California Institute of Technology, the University of California, and the National Aeronautics and Space Administration.