  Previous work has demonstrated that at a given stellar mass, quiescent
galaxies are more strongly clustered than star-forming galaxies. The
contribution to this signal from central, as opposed to satellite, galaxies is
not known, which has strong implications for galaxy evolution models. To
investigate the contribution from central galaxies, here we present
measurements of the clustering of isolated primary (IP) galaxies, used as a
proxy for central galaxies, at ${0.2<z<0.9}$ with data from the PRIMUS galaxy
redshift survey. Using a sample of spectroscopic redshifts for $\sim60,000$
galaxies with ${M_*\gtrsim10^9~M_\odot}$ covering 5 deg$^2$ on the sky, we
define IP galaxies using isolation cuts in spatial proximity and stellar mass
of nearby galaxies. We find that at fixed stellar mass, quiescent IP galaxies
are more strongly clustered than star-forming IP galaxies at $z\sim0.35$
$(10\sigma)$. Using mock galaxy catalogs based on recent halo occupation models
of Behroozi et al. (2018) and designed to replicate the parameters of the
PRIMUS survey dataset, we find that these clustering differences are due in
part to quiescent central galaxies being more strongly clustered than
star-forming central galaxies. This is consistent with either distinct
stellar-to-halo mass relations for quiescent and star-forming central galaxies,
and/or central galaxy assembly bias. We additionally use mock catalogs to
assess the dependence of both incompleteness and satellite galaxy contamination
in the IP galaxy samples on redshift, galaxy type, and stellar mass, and
demonstrate how isolation criteria yield biased subsamples of central galaxies
via {\it environmental incompleteness}, or the preferential exclusion of
central galaxies in overdense environments.
