In the 110 pb^-1 Run I data sample, using three complementary flavor-tagging algorithms CDF has made a new measurement of the CP-violating symmetry sin(2 Beta) = 0.79^+0.41_ -0.44. This corresponds to the limit sin(2 Beta) > -0.08 at 95 percent confidence level. This result agres well with predictions from indirect constraints based on fits of elements of the CKM matrix.