We report the first observation of two narrow resonances with
states of orbitally excited (L = 1) B_s mesons using 1 fb-1 of p anti-p
collisions at s**(1/2) = 1.96 TeV collected with the CDF II detector
at the Fermilab Tevatron. We use two-body decays into K- and B+ mesons
reconstructed as B+ --> J/psi K+, J/psi --> mu+ mu- or B+ -->
D-bar0 pi++, D-bar0 --> K+ pi+-. We deduce the masses of the two
states to be m(B_s1) = 5829.4 +/- 0.7 MeV/c2 and m(B*_s2) = 5839.7 +/-
0.7 MeV/c2.