  We report measurements of the ^{115}In nuclear spin-lattice relaxation rate
(1/T_1) between T=0.09 K and 100 K in the new heavy fermion (HF) compound
CeIrIn_5. At 0.4 K < T < 100 K, 1/T_1 is strongly T-dependent, which indicates
that CeIrIn_5 is much more itinerant than known Ce-based HFs. We find that
1/T_1T, subtracting that for LaIrIn_5, follows a 1/(T+\theta)^{3/4} variation
with \theta=8 K. We argue that this novel feature points to anisotropic, due to
a layered crystal structure, spin fluctuations near a magnetic ordering. The
bulk superconductivity sets in at 0.40 K below which the coherence peak is
absent and 1/T_1 follows a T^3 variation, which suggests unconventional
superconductivity with line-node gap.
