  Single-layer MoS$_2$ and similar dichalcogenides are direct-gap
semiconductors with a peculiar band structure: the direct gap is situated at
the K$^+$ and K$^-$ points in the Brillouin zone, with a large valence-band
spin splitting. Optical selection rules allow for valley-selective interband
excitation using near-resonant, circularly polarized excitation. Here, we
present time-resolved pump-probe experiments in which we study the carrier and
valley dynamics in a mechanically exfoliated single-layer MoS$_2$ flake at low
temperatures. Under resonant excitation conditions, we find that the valley
lifetime exceeds the photocarrier lifetime, indicating the creation of a
resident valley polarization. For highly nonresonant excitation, the valley
polarization decays within the photocarrier lifetime.
