We report the observation of the Xi(c)(*+) state decaying into Xi(c)(0)pi(+) with Xi(c)(0 )-->( )Lambda (K) over bar(0)pi(+)pi(-) or Lambda K(-)pi(+)pi(+)pi(-). We have observed 47 +/- 11 candidate events for the Xi(c)(*+) state and measured its mass to be 177.1 +/- 0.5 +/- 1.1 MeV/c(2) above the Xi(c)(0) mass. We have also measured the Xi(c)(0) mass to be 2470.0 +/- 2.8 +/- 2.6 MeV/c(2). (C) 1998 Published by Elsevier Science B.V. All rights reserved.