We demonstrate via a muon spin rotation experiment that the electronic ground state of the iridium spinel compound, CuIr$_2$S$_4$, is not the presumed spin-singlet state but a novel paramagnetic state, showing a quasistatic spin glass-like magnetism below ~100 K. Considering the earlier indication that IrS$_6$ octahedra exhibit dimerization associated with the metal-to-insulator transition below 230 K, the present result suggests that a strong spin-orbit interaction may be playing an important role in determining the ground state that accompanies magnetic frustration.
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