We present a measurement of the time-dependent asymmetry in the
rate for B-bar^0 versus B^0 decays to J/psi K^0_s.  The data sample consists
of 198 +/- 17 B^0/B-bar^0 decays collected by the CDF detector in ppbar
collisions at the Fermilab Tevatron, where the initial b flavor has been
determined by a same-side flavor tagging technique.  This asymmetry is
interpreted in the Standard Model as a measurement of the CP-violation
parameter sin(2 beta).  Our analysis results in sin(2 beta) = 1.8 +/-
1.1(stat) +/- 0.3(syst).