[en] We present the results of an extensive Hubble Space Telescope imaging study of 105, mostly Swift, long-duration gamma-ray bursts (LGRBs) spanning $0.03\lesssim <!--\; ???\; -->z\lesssim <!--\; ???\; -->9.4$, which were localized using relative astrometry from ground- and space-based afterglow observations. We measure the distribution of LGRB offsets from their host centers and their relation to the underlying host light distribution. We find that the host-normalized offsets of LGRBs are more centrally concentrated than expected for an exponential disk profile, $⟨<!--\; ???\; -->R/R_h⟩<!--\; ???\; -->$ = 0.63, and in particular they are more concentrated than the underlying surface brightness profiles of their host galaxies and more concentrated than supernovae. The fractional flux distribution, with a median of 0.78, indicates that LGRBs prefer some of the brightest locations in their host galaxies but are not as strongly correlated as previous studies indicated. Importantly, we find a clear correlation between offset and fractional flux, where bursts at offsets $R/R_h\lesssim <!--\; ???\; -->0.5$ exclusively occur at fractional fluxes $\gtrsim <!--\; ???\; -->0.6$, while bursts at $R/R_h\gtrsim <!--\; ???\; -->0.5$ have a uniform fractional flux distribution. This indicates that the spatial correlation of LGRBs with bright star-forming regions seen in the full sample is dominated by the contribution from bursts at small offset and that LGRBs in the outer parts of galaxies show no preference for unusually bright regions. We conclude that LGRBs strongly prefer the bright, inner regions of their hosts, indicating that the star formation taking place there is more favorable for LGRB progenitor production. This indicates that environmental factors beyond metallicity, such as binary interactions or IMF differences, may operate in the central regions of LGRB hosts.