The CKM mechanism is well established as the dominant mechanism
for CP violation, which was first discovered in the neutral kaons in 1964.
To search for new sources of CP violation, one can exploit a handful
of systems in which the standard model makes a precise prediction of
CP violation.  In the B0(s) --> J/psi phi system, CP violation in the
interference of mixing and decay is precisely predicted in the standard
model, the prediction being very close to zero.  The CDF experiment
reconstructs about 2000 signal events in 1.35 fb-1 of luminosity.
We obtain a confidence region in the space of the parameters beta_s,
the CP phase, and Delta Gamma, the width difference.  This result is
1.5 sigma from the standard model prediction.