We present the first precise measurement of the Bs0-Bs0 oscillation frequency Deltams. We use 1 fb-1 of data from pp collisions at sqrts=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 Bs0-Bs0 oscillations. The probability that random fluctuations could produce a comparable signal is 0.2%. Under the hypothesis that the signal is due to Bs0-Bs0 oscillations, we measure Deltams=17.31(-0.18)+0.33(stat)+/-0.07(syst) ps-1 and determine |Vtd/Vts|=0.208(-0.002)+0.001(expt)-0.006(+0.008)(theor).