We report on the first measurement of the flux of upgoing muons resulting from interactions of atmospheric neutrinos in the rock below MACRO. The ratio of the observed to the expected number of events integrated over all nadir angles is 0.73 +/- .09(stat) +/- 0 .06(sys) +/- 12(theor.). The flux of upgoing muons as a function of nadir angle is presented and compared to Monte Carlo expectations. At the 90% confidence level, the data are consistent with no neutrino oscillations or some possible oscillation hypotheses with the parameters suggested by the Kamiokande contained-event analysis.
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