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We present the first uniform treatment of long duration gamma-ray burst (GRB) host galaxy detections and upper limits over the redshift range , a key epoch for observational and theoretical efforts to understand the processes, environments, and consequences of early cosmic star formation (SF). We contribute deep imaging observations of 13 GRB positions yielding the discovery of 8 new host galaxies. We use this data set in tandem with previously published observations of 31 further GRB positions to estimate or constrain the host galaxy rest-frame ultraviolet (UV; Å) absolute magnitudes . We then use the combined set of 44 estimates and limits to construct the luminosity function (LF) for GRB host galaxies over and compare it to expectations from Lyman break galaxy (LBG) photometric surveys with the Hubble Space Telescope. Adopting standard prescriptions for the luminosity dependence of galaxy dust obscuration (and hence, total SF rate), we find that our LF is compatible with LBG observations over a factor of 600× in host luminosity, from = −22.5 mag to >−15.6 mag, and with extrapolations of the assumed Schechter-type LF well beyond this range. We review proposed astrophysical and observational biases for our sample, and find that they are for the most part minimal. We therefore conclude, as the simplest interpretation of our results, that GRBs successfully trace UV metrics of cosmic SF over the range . Our findings suggest that GRBs provide an accurate picture of star formation processes from out to the highest redshifts. [ABSTRACT FROM AUTHOR]