  We constrain the newly-introduced decorated Halo Occupation Distribution
(HOD) model using SDSS DR7 measurements of projected galaxy clustering or
r-band luminosity threshold samples. The decorated HOD is a model for the
galaxy-halo connection that augments the HOD by allowing for the possibility of
galaxy assembly bias: galaxy luminosity may be correlated with dark matter halo
properties besides mass, Mvir. We demonstrate that it is not possible to rule
out galaxy assembly bias using DR7 measurements of galaxy clustering alone.
Moreover, galaxy samples with Mr < -20 and Mr < -20.5 favor strong central
galaxy assembly bias. These samples prefer scenarios in which
high-concentration are more likely to host a central galaxy relative to
low-concentration halos of the same mass. We exclude zero assembly bias with
high significance for these samples. Satellite galaxy assembly bias is
significant for the faintest sample, Mr < -19. We find no evidence for assembly
bias in the Mr < -21 sample. Assembly bias should be accounted for in galaxy
clustering analyses or attempts to exploit galaxy clustering to constrain
cosmology. In addition to presenting the first constraints on HOD models that
accommodate assembly bias, our analysis includes several improvements over
previous analyses of these data. Therefore, our inferences supersede
previously-published results even in the case of a standard HOD analysis.
