We propose a new scenario of baryogenesis in which baryon number is an exact symmetry of the fundamental Lagrangian. If the global U(1) symmetry associated with baryon number is spontaneously broken at early times (when the temperature was of order 1--100 GeV) then the out-of-equilibrium decay of baryonic scalar particles can yield a cosmic baryon asymmetry in ordinary matter. This baryon number is exactly compensated by antibaryon number in the vacuum. At low temperatures, the symmetry is restored, and the antibaryons show up as neutral (antibaryonic) scalar particles or as nontopological solitons.