Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; We provide the most precise measurement of the WW production cross section in pp collisions to date at a center of mass energy of 1.96 TeV, and set limits on the associated trilinear gauge couplings. The WW -> l nu l(')nu (l, l(')=e, mu) decay channels are analyzed in 1 fb(-1) of data collected by the D0 detector at the Fermilab Tevatron Collider. The measured cross section is sigma(pp -> WW)=11.5 +/- 2.1(stat+syst)+/- 0.7(lumi) pb. One- and two-dimensional 95% C.L. limits on trilinear gauge couplings are provided.