We report measurements of the 115 In nuclear spin-lattice relaxation rate (1/T1) between T =0.09 K and 100 K in the new heavy fermion (HF) compound CeIrIn5. At 0.4 K ≤ T ≤ 100 K, 1/T1 is strongly T -dependent, which indicates that CeIrIn5 is much more itinerant than known Ce-based HFs. We find that 1/T1T , subtracting that for LaIrIn5, follows a ( 1 T +θ ) 3 4 variation with θ=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/T1 follows a T 3 variation, which suggests unconventional superconductivity with line-node gap. PACS: 74.25.Ha, 74.70Tx, 76.60.Gv The emergence of superconductivity near a magnetic instability in cerium (Ce)-based heavy fermion (HF) compounds is one of the most intriguing phenomena in strongly correlated electron systems. Except for CeCu 2 Si 2 which is superconducting at ambient pressure with T c =0. . In spite of efforts and progress, however, knowledge about this class of superconductors is still limited because of difficult experimental conditions. The recently discovered new family of Ce-based heavy electron systems, CeMIn 5 (M=Rh, Ir) with M=Ir being a superconductor already at ambient pressure [6,7], provides new opportunities for studying the nature of the superconductivity in the vicinity of a magnetic instability, the interplay between magnetic excitations and superconductivity, etc. In particular, CeIrIn 5 is suitable for studies using microscopic experimental probes that can be applied more easily at ambient pressure.CeMIn 5 (M=Rh, Ir) consists of alternating layers of CeIn 3 and MIn 2 . CeRhIn 5 is an antiferromagnet with T N =3.8 K but becomes superconducting below T c =2.1 K under pressures larger than 1.6 GPa [6]. In CeIrIn 5 , the resistivity is already zero at ambient pressure below 1.2 K, but the Meissner effect and the jump in the specific heat are found only at 0.4 K [7]. The electronic specific heat coefficient γ is found to be 750 mJ/mol K 2 [7], which suggests a large mass enhancement. Recent de Haas-van Alphen Oscillation in CeIrIn 5 also reveals a cyclotron mass that is ∼20 times larger than the band mass, consistent with the specific heat result [8].In this Letter, we report a measurement using local probe, the 115 In nuclear quadrupolar resonance (NQR) study in CeIrIn 5 down to 90 mK, at zero magnetic field.From the temperature (T ) dependence of the nuclear spin lattice relaxation rate (1/T 1 ), we find that CeIrIn 5 is much more itinerant than known Ce-compounds such as CeCu 2 Si 2 [9], and show that this compound is located near a magnetic ordering with anisotropic spin fluctuations due to the layered crystal structure. No anomaly was found at 1.2 K in the NQR quantities, but 1/T 1 shows an abrupt decrease at 0.40 K below which the NQR intensity also decreases as does the ac susceptibility, confirming a bulk superconductivity below T c =0.40 K. The lack of coherence peak in 1/T...