The spin dynamics in CsPbBr3 lead halide perovskite nanocrystals are studied by picosecond pump-probe Faraday rotation in an external magnetic field. Coherent Larmor precession of electrons and holes with spin dephasing times of ∼600 ps is detected in a transversal magnetic field. The longitudinal spin relaxation time in weak magnetic fields reaches 80 ns at a temperature of 5 K. In this regime, the carrier spin dynamics is governed by nuclear spin fluctuations characterized by an effective hyperfine field strength of 25 mT. The Landé factors determining the carrier Zeeman splittings are ge = +1.73 for electrons and gh = +0.83 for holes. A comparison with a CsPbBr3 polycrystalline film and bulk single crystals evidences that the spatial confinement of electrons and holes in the nanocrystals only slightly affects their g factors and spin dynamics.