  We present NMR measurements of the layered nitride superconductor Li_xZrNCl.
The nuclear spin-lattice relaxation rate, 1/T_1, shows that the coherence peak
is strongly suppressed in Li_xZrNCl in contrast to conventional BCS
superconductors. In the lightly-doped region close to the insulating state, the
system shows a gap-like behavior, i.e., pseudogap, that is characterized by a
reduction in the magnitude of the Knight shift and 1/T_1T. A higher
superconducting (SC) transition temperature, T_c, is achieved by coexisting
with the pseudogap state. These unusual behaviors, which deviate from the
ordinary BCS framework, are the key ingredients to understanding the SC
mechanism of Li_xZrNCl.
