Granular polycrystalline silicon is disclosed, which has a convexity of 0.850-1.000 and a chlorine content of 10-40 ppmw. Also disclosed is a process for producing granular polycrystalline silicon in a fluidized bed reactor, which includes: (a) fluidization of silicon seed particles by gas flow in a fluidized bed heated by a heating apparatus, (b) addition of a silicon- and halogen-containing reaction gas resulting in pyrolytic deposition of elemental silicon on heated seed particle surfaces, (c) forming the granular polycrystalline silicon, (d) removing from the reactor particles and offgas containing hydrogen halide, and (e) metered addition of fresh seed particles. The hydrogen halide concentration in the offgas is determined as the controlled variable. The rate of metered addition of fresh seed particles and heating output of the heating apparatus are controlled as manipulated variables to keep the hydrogen halide concentration in the offgas within an above-defined range during operation.