We present the first precise measurement of the B0s-B0s oscillation frequency Δms. We use 1  fb−1 of data from pp collisions at s√=1.96  TeV collected with the CDF II detector at the Fermilab Tevatron. The sample contains signals of 3600 fully reconstructed hadronic Bs decays and 37 000 partially reconstructed semileptonic Bs decays. We measure the probability as a function of proper decay time that the Bs decays with the same, or opposite, flavor as the flavor at production, and we find a signal consistent with B0s-B0s oscillations. The probability that random fluctuations could produce a comparable signal is 0.2%. Under the hypothesis that the signal is due to B0s-B0s oscillations, we measure Δms=17.31+0.33−0.18(stat)±0.07(syst)  ps−1 and determine |Vtd/Vts|=0.208+0.001−0.002(expt)+0.008−0.006(theor).