We present results of a dark matter search performed with a 0.6 kg day exposure of the DAMIC experiment at the SNOLAB underground laboratory. We measured the energy spectrum of ionization events in the bulk silicon of charge-coupled devices (CCDs) down to a signal of 60 eV electron-equivalent. The data is consistent with radiogenic backgrounds, and constraints on the spin-independent WIMP-nucleon elastic-scattering cross-section are accordingly placed. Cross-sections relevant to the potential signal from the CDMS-II Si experiment are excluded using the same target for the first time. This result, obtained with a limited exposure, demonstrates the potential to explore the low-mass WIMP region (<10 GeV/$c^{2}$) of the upcoming DAMIC100, a 100 g detector currently being installed in SNOLAB.
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