The production of J/ψ mesons in continuum e^+e^− annihilations has been studied with the BABAR detector at energies near the Υ(4S) resonance. The mesons are distinguished from J/ψ production in B decays through their center-of-mass momentum and energy. We measure the cross section e^+e^− → J/ψX to be 2.52±0.21±0.21pb. We set a 90% C.L. upper limit on the branching fraction for direct Υ(4S) → J/ψX decays at 4.7×10^(-4)
