We present early-time optical through infrared photometry of the bright Swift gamma-ray burst (GRB) 080607, starting only 6 s following the initial trigger in the rest frame. Complemented by our previously published spectroscopy, this high-quality photometric data set allows us to solve for the extinction properties of the redshift 3.036 sightline, giving perhaps the most detailed information to date on the ultraviolet continuum absorption properties of any sightline outside our Local Group. The extinction properties are not adequately modeled by any ordinary extinction template (including the average Milky Way, Large Magellanic Cloud, and Small Magellanic Cloud curves), partially because the 2175 ̊A feature (while present) is weaker by about a factor of two than when seen under similar circumstances locally. However, the spectral energy distribution is exquisitely fitted by the more general Fitzpatrick & Massa parameterization of Local-Group extinction, putting it in the same family as some peculiar Milky Way extinction curves. After correcting for this (considerable, A$_V$ = 3.3 ± 0.4 mag) extinction, GRB 080607 is revealed to have been among the most optically luminous events ever observed, comparable to the naked-eye burst GRB 080319B. Its early peak time (t $_rest$ < 6 s) indicates a high initial Lorentz factor (Γ>600), while the extreme luminosity may be explained in part by a large circumburst density. Only because of its early high luminosity could the afterglow of GRB 080607 be studied in such detail in spite of the large attenuation and great distance, making this burst an excellent prototype for the understanding of other highly obscured extragalactic objects, and of the class of ``dark’’ GRBs in particular.