  We report on novel antiferromagnetic (AFM) and superconducting (SC)
properties of noncentrosymmetric CePt3Si through measurements of the 195Pt
nuclear spin-lattice relaxation rate 1/T_1. In the normal state, the
temperature (T) dependence of 1/T1 unraveled the existence of low-lying levels
in crystal-electric-field multiplets and the formation of a heavy fermion (HF)
state. The coexistence of AFM and SC phases, that emerge at TN = 2.2 K and Tc =
0.75 K, respectively, takes place on a microscopic level. CePt3Si is the first
HF superconductor that reveals a peak in 1/T1 just below Tc and, additionally,
does not follow the T^3 law that used to be reported for most unconventional HF
superconductors. We remark that this unexpected SC characteristics may be
related with the lack of an inversion center in its crystal structure.
