We study deterministic magnetic reversal of a perpendicularly magnetized Co layer in a Co/MgO/Ta nanosquare driven by spin Hall torque from an in-plane current flowing in an underlying Pt layer. The rate-limiting step of the switching process is domain wall (DW) depinning by spin Hall torque via a thermally assisted mechanism that eventually produces full reversal by domain expansion. An in-plane applied magnetic field collinear with the current is required, with the necessary field scale set by the need to overcome DW chirality imposed by the Dzyaloshinskii-Moriya interaction. Once Joule heating is taken into account the switching current density is quantitatively consistent with a spin Hall angle θSH≈0.07 for 4 nm of Pt. © 2014 American Physical Society.