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 one 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 weakly interacting massive particle (WIMP)-proton spin-dependent cross section at 3.4×10^{-41} cm^{2} for a 30-GeV c^{-2} WIMP, more than 1 order of magnitude improvement from previous PICO results.