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[Abridged] We present the results of an extensive Hubble Space Telescope(HST) imaging study of ~100 Swift long-duration gamma-ray bursts (LGRBs)spanning 0.03 < z < 9.4 using relative astrometry from afterglow observationsto locate the bursts within their host galaxies. We measure the distribution ofLGRB offsets from their host centers, as well as their relation to theunderlying host light distribution. We find that the host-normalized offsets(R/R_h) of LGRBs are more centrally concentrated than expected for anexponential disk profile, with a median of 0.67, and in particular they aremore concentrated than the underlying surface brightness profiles of their hostgalaxies. The distribution of offsets is inconsistent with the distribution forType II supernovae (SNe) but consistent with the distribution for Type Ib/cSNe. The fractional flux distribution, with a median of 0.75, indicates thatLGRBs prefer some of the brightest locations in their host galaxies but are notas strongly correlated as previous studies indicated. More importantly, we finda clear correlation between the offset and fractional flux, where bursts atR/R_h < 0.5 exclusively occur at fractional fluxes > 0.6 while bursts at R/R_h> 0.5 uniformly trace the light of their hosts. This indicates that the spatialcorrelation of LGRB locations with bright star forming regions seen in the fullsample is dominated by the contribution from bursts at small offset and thatLGRBs in the outer parts of galaxies show no preference for unusually brightstar forming regions. We conclude that LGRBs strongly prefer the bright, innerregions of their hosts indicating that the star formation taking place there ismore favorable for LGRB progenitor production. This indicates that anotherenvironmental factor beyond metallicity, such as binary interactions or IMFdifferences, may be operating in the central regions of LGRB hosts.

The Offset and Host Light Distributions of Long Gamma-Ray Bursts: A New View from HST Observations of Swift Bursts