The production of Ξ (1321) ^- and Ξ ¯ (1321) ⁺ hyperons in inelastic p+p interactions is studied in a fixed target experiment at a beam momentum of 158 Ge/c. Double differential distributions in rapidity y and transverse momentum p_T are obtained from a sample of 33M inelastic events. They allow to extrapolate the spectra to full phase space and to determine the mean multiplicity of both Ξ ^- and Ξ ¯ ⁺. The rapidity and transverse momentum spectra are compared to transport model predictions. The Ξ ^- mean multiplicity in inelastic p+p interactions at 158 Ge/c is used to quantify the strangeness enhancement in A+A collisions at the same centre-of-mass energy per nucleon pair.