The forward-backward asymmetry of charm quark production has been measured at an average energy of 58.4 GeV with the VENUS detector at the TRISTAN e+e- collider. The charm quarks were identified through reconstruction of charged D* mesons using the mass difference between the D* and D0 mesons. The measured charge asymmetry, -0.49(-0.17)+0.19 +/- 0.04, is consistent with the prediction of the standard theory. The corresponding axial-vector coupling constant is 1.03(-0.35)+0.40 +/- 0.07.