Using the sample from the Redshift One LDSS-3 Emission line Survey (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 Chandra Deep Field South field. Our spectroscopic sample consists of 312 galaxies with KAB < 24, corresponding to stellar mass log(M*/M⊙) > 8.5, and with [O ii] derived SFR > 0.3 M⊙ yr−1, at 0.889 ≤z≤ 1.149. The results have been compared directly with the Sloan Digital Sky Survey Stripe 82 sample at 0.032 ≤z≤ 0.05. For star-forming galaxies, we confirm that there is little correlation between SFR and density at z∼ 0. However, for the lowest mass galaxies in our z∼ 1 sample, those with log(M*/M⊙) < 10, we find that both the median SFR and sSFR 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.