It has long remained elusive whether CuCo$_{2}$S$_{4}$ thiospinel shows bulk superconductivity. Here we clarify the issue by studying on the samples of sulfur-deficient CuCo$_{2}$S$_{3.7}$ and sulfurized CuCo$_{2}$S$_{4}$. The sample CuCo$_{2}$S$_{3.7}$ has a smaller lattice constant of $a=9.454$ {AA}, and it is not superconducting down to 1.8 K. After a full sulfurization, the $a$ axis of the thiospinel phase increases to 9.475 {AA}, and the thiospinel becomes nearly stoichiometric CuCo$_{2}$S$_{4}$, although a secondary phase of slightly Cu-doped CoS$_2$ forms. Bulk superconductivity at 4.2 K and Pauli paramagnetism have been demonstrated for the sulfurized CuCo$_{2}$S$_{4}$ by the measurements of electrical resistivity, magnetic susceptibility, and specific heat.
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