We present the first sample of 31GHz selected sources to flux levels of 1mJy. From late 2005 to mid-2007, the Sunyaev-Zel'dovich Array observed 7.7deg^2^ of the sky at 31GHz to a median rms of 0.18mJy/beam. We identify 209 sources at greater than 5{sigma} significance in the 31GHz maps, ranging in flux from 0.7mJy to ~200mJy. Archival NVSS data at 1.4GHz and observations at 5GHz with the Very Large Array are used to characterize the sources. We determine the maximum-likelihood integrated source count to be N(>S)=(27.2+/-2.5)deg^-2^x(S_mJy_)^-1.18+/-0.12^ over the flux range 0.7-15mJy. This result is significantly higher than predictions based on 1.4GHz selected samples, a discrepancy which can be explained by a small shift in the spectral index distribution for faint 1.4GHz sources. From comparison with previous measurements of sources within the central arcminute of massive clusters, we derive an overdensity of 6.8+/-4.4, relative to field sources.