Nuclear quadrupole resonance measurements were performed on the heavy-fermion superconductor Ce 2PdIn 8. Above the Kondo coherence temperature T coh30 K, the spin-lattice relaxation rate 1/T 1 is temperature independent, whereas at lower temperatures, down to the onset of superconductivity at T c=0.64 K, it is nearly proportional to T1 /2. Below T c, 1/T 1 shows no coherence peak and decreases as T3 down to 75 mK. All these findings indicate that Ce 2PdIn 8 is close to the antiferromagnetic quantum critical point, and the superconducting state has an unconventional character with line nodes in the superconducting gap. © 2012 American Physical Society.