We report the first measurement of charmed-hadron (D(0)) production via the hadronic decay channel (D(0) → K(-) + π(+)) in Au+Au collisions at sqrt[s(NN)] = 200 GeV with the STAR experiment. The charm production cross section per nucleon-nucleon collision at midrapidity scales with the number of binary collisions, N(bin), from p+p to central Au+Au collisions. The D(0) meson yields in central Au + Au collisions are strongly suppressed compared to those in p+p scaled by N(bin), for transverse momenta p(T) > 3 GeV/c, demonstrating significant energy loss of charm quarks in the hot and dense medium. An enhancement at intermediate p(T) is also observed. Model calculations including strong charm-medium interactions and coalescence hadronization describe our measurements.