We report the observation of two narrow resonances consistent with states of orbitally excited (L=1) B_(s) mesons using 1 fb;(-1) of pp[over ] collisions at sqrt[s]=1.96 TeV collected with the Collider Detector at Fermilab II detector at the Fermilab Tevatron. We use two-body decays into K- and B+ mesons reconstructed as B(+)-->J/psiK(+), J/psi-->mu(+)mu(-) or B(+)-->D[over ](0)pi(+), D[over ](0)-->K(+)pi(-). We deduce the masses of the two states to be m(B_(s1))=5829.4+/-0.7 MeV/c(2) and m(B_(s2);(*))=5839.6+/-0.7 MeV/c;(2).