Using time-resolved Kerr rotation, we measure the spin-valley dynamics of resident electrons and holes in single charge-tunable monolayers of the archetypal transition-metal dichalcogenide (TMD) semiconductor WSe2. In the n-type regime, we observe long (∼130  ns) polarization relaxation of electrons that is sensitive to in-plane magnetic fields By, indicating spin relaxation. In marked contrast, extraordinarily long (∼2  μs) polarization relaxation of holes is revealed in the p-type regime, which is unaffected by By, directly confirming long-standing expectations of strong spin-valley locking of holes in the valence band of monolayer TMDs. Supported by continuous-wave Kerr spectroscopy and Hanle measurements, these studies provide a unified picture of carrier polarization dynamics in monolayer TMDs, which can guide design principles for future valleytronic devices.