We present 5201 radial-velocity measurements of 1144 stars, as part of an ongoing study of the young (150 Myr) open cluster M35 (NGC 2168). We have observed M35 since 1997, using the Hydra Multi-Object Spectrograph on the WIYN 3.5m telescope. Our stellar sample covers main-sequence stars over a magnitude range of 13.0<V<16.5 (1.6 - 0.8 Msun) and extends spatially to a radius of 30 arcminutes (7 pc in projection at a distance of 805 pc or 4 core radii). Due to its youth, M35 provides a sample of late-type stars with a range of rotation periods. Therefore, we analyze the radial-velocity measurement precision as a function of the projected rotational velocity. For narrow-lined stars (v sin i < 10 km/s), the radial velocities have a precision of 0.5 km/s, which degrades to 1.0 km/s for stars with v sin i = 50 km/s. The radial-velocity distribution shows a well-defined cluster peak with a central velocity of -8.16 +/- 0.05 km/s, permitting a clean separation of the cluster and field stars. For stars with >=3 measurements, we derive radial-velocity membership probabilities and identify radial-velocity variables, finding 360 cluster members, 55 of which show significant radial- velocity variability. Using these cluster members, we construct a color-magnitude diagram for our stellar sample cleaned of field star contamination. We also compare the spatial distribution of the single and binary cluster members, finding no evidence for mass segregation in our stellar sample. Accounting for measurement precision, we place an upper limit on the radial-velocity dispersion of the cluster of 0.81 +/- 0.08 km/s. After correcting for undetected binaries, we derive a true radial-velocity dispersion of 0.65 +/- 0.10 km/s.