  Using the sample from the \it Redshift One LDSS3 Emission line Survey \rm
(ROLES), we probe the dependence of star formation rate (SFR) and specific star
formation rate (sSFR) as a function of stellar mass $M_*$ and environment as
defined by local galaxy density, in the CDFS field. Our spectroscopic sample
consists of 312 galaxies with $K_{AB}<24$, corresponding to stellar mass
$\log(M_*/M_{\sun})>8.5$, and with [OII] derived star-formation rates
SFR$>0.3M_{\sun}/$yr, at $0.889\leq z \leq 1.149$. The results have been
compared directly with the Sloan Digital Sky Survey Stripe 82 sample at
$0.032\leq z \leq 0.05$. For star-forming galaxies, we confirm that there is
little correlation between SFR and density at $z\sim 0$. However, for the
lowest mass galaxies in our $z\sim 1$ sample, those with
$\log(M_*/M_{\sun})<10$, we find that both the median SFR and specific SFR {\it
increase} significantly with increasing local density. The "downsizing" trend
for low mass galaxies to be quenched progressively later in time appears to be
more pronounced in moderately overdense environments. Overall we find that the
evolution of star-formation in galaxies is most strongly driven by their
stellar mass, with local galaxy density playing a role that becomes
increasingly important for lower mass galaxies.
