  We begin the study of unitary representations of Hecke algebras of complex
reflections groups. We obtain a complete classification for the Hecke algebra
of the symmetric group $\mathfrak{S}_n$ over the complex numbers.
Interestingly, the unitary representations in the category $\OO$ for the
rational Cherednik algebra of type A studied in \cite{ESG} correspond to the
unitary representations of the corresponding Hecke algebra via the KZ functor
defined in \cite{GGOR}.
