We report the observation of prompt J/psi via double cc; production from the e+e- continuum. In this process one cc; pair fragments into a J/psi meson while the remaining pair either produces a charmonium state or fragments into open charm. Both cases have been experimentally observed. We find cross sections of sigma[e+e- -->J/psieta(c)(gamma)]xB(eta(c)-->>or=4 charged)=(0.033(+0.007)(-0.006)+/-0.009) pb and sigma(e+e- -->J/psiD(*+)X)=(0.53(+0.19)(-0.15)+/-0.14) pb and infer sigma(e+e- -->J/psicc;)/sigma(e+e- -->J/psiX)=0.59(+0.15)(-0.13)+/-0.12. These results are obtained from a 46.2 fb(-1) data sample collected near the Upsilon(4S) resonance, with the Belle detector at the KEKB collider.