The cross section for WW production is measured and limits on anomalous WWgamma and WWZ trilinear gauge couplings are set using WW → ee/emu/mumu events collected by the Run II DO detector at the Fermilab Tevatron Collider corresponding to 1 fb-1 of integrated luminosity at s = 1.96 TeV. Across the three final states, 108 candidate events are observed with 40.8+/-3.8 total background expected, consistent with sigma( pp → WW) = 11.6 +/- 1.8 (stat) +/- 0.7 (syst) +/- 0.7 (lumi) pb. Using a set of SU(2)L ⊗ U(1) Y conserving constraints, the one-dimensional 95% C.L. limits on trilinear gauge couplings are -0.63 < Deltakappagamma < 0.99, -0.15 < lambdagamma < 0.19, and -0.14 < Delta gZ1 < 0.34.