New results are reported from the operation of the PICO-60 dark matter detector, a bubble chamber filled with 52 kg of C$_3$F$_8$ located in the SNOLAB underground laboratory. As in previous PICO bubble chambers, PICO-60 C$_3$F$_8$ exhibits excellent electron recoil and alpha decay rejection, and the observed multiple-scattering neutron rate indicates a single-scatter neutron background of less than 1 event per month. A blind analysis of an efficiency-corrected 1167-kg-day exposure at a 3.3-keV thermodynamic threshold reveals no single-scattering nuclear recoil candidates, consistent with the predicted background. These results set the most stringent direct-detection constraint to date on the WIMP-proton spin-dependent cross section at 3.4 $times$ 10$^{-41}$ cm$^2$ for a 30-GeV$thinspace$c$^{-2}$ WIMP, more than one order of magnitude improvement from previous PICO results.
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