  We present the first study of the time-dependent CP-violating asymmetry in B0
-> J/psi pi0 decays using e+e- annihilation data collected with the BaBar
detector at the Upsilon(4S) resonance during the years 1999-2002 at the PEP-II
asymmetric-energy B Factory at SLAC. Using approximately 88 million BBbar
pairs, our results for the coefficients of the cosine and sine terms of the CP
asymmetry are C_(J/psi pi0) = 0.38 +/- 0.41 (stat) +/- 0.09 (syst) and S_(J/psi
pi0) = 0.05 +/- 0.49 (stat) +/- 0.16 (syst).
