We report the results of our study of a recently synthesized honeycomb iridate ${\mathrm{Na}}_x{\mathrm{IrO}}_3$ $(0.60\le x\le 0.80)$. Single-crystal ${\mathrm{Na}}_x{\mathrm{IrO}}_3$ adopts a honeycomb lattice noticeably without distortions and stacking disorder inherently existent in its sister compound ${\mathrm{Na}}_2{\mathrm{IrO}}_3$. The oxidation state of the Ir ion is a mixed valence state resulting from a majority ${\mathrm{Ir}}^{5+}\left(5d^4\right)$ ion and a minority ${\mathrm{Ir}}^{6+}\left(5d^3\right)$ ion. ${\mathrm{Na}}_x{\mathrm{IrO}}_3$ is a Mott insulator likely with a predominant pseudospin $=1$ state. It exhibits an effective moment of $1.1{\mu }_{\mathrm{B}}/\mathrm{Ir}$ and a Curie-Weiss temperature of −19 K but with no discernible long-range order above 1 K. The physical behavior below 1 K features two prominent anomalies at $T_h=0.9\mathrm{K}$ and $T_l=0.12\mathrm{K}$ in both the heat capacity and AC magnetic susceptibility. Intermediate between $T_h$ and $T_l$ lies a pronounced temperature linearity of the heat capacity with a large slope of $77\mathrm{mJ}/\mathrm{mole}{\mathrm{K}}^2$, a feature expected for highly correlated metals but not at all for insulators. These results along with a comparison drawn with the honeycomb lattices ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and ${\left({\mathrm{Na}}_{0.2}{\mathrm{Li}}_{0.8}\right)}_2{\mathrm{IrO}}_3$ point to an exotic ground state in proximity to a possible Kitaev spin liquid.

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• Quantum spin liquid
• Honeycomb lattice
• Iridates
• Kitaev model