The B0 anti-B0 average mixing parameter chi has been extracted from e mu and ee events produced in p anti-p collisions at s**(1/2) = 1.8 TeV. In a sample of 900 e mu events, the like-sign to opposite-sign charge ratio R is measured to be 0.556 +- 0.048(stat) +0.035 - 0.042(sys). In the absence of mixing, the expected value of P would be 0.23+-0.06. The corresponding number for 212 ee events is 0.573 += 0.116 (stat) +- (sys) with an expected non-mixing value of 0.24+-0.07. The observed excess in R leads to a combined determination of chi = 0.176 +- 0.31 (stat+sys) +- (model), where the last uncertainty is due to Monte Carlo modeling.