  The abundant production of lepton pairs via $J/\Psi$ creation at COMPASS,
$\pi ^\pm \, p^\uparrow \to J/\Psi \, X \to \ell^+ \ell^- X$, allows a
measurement of the transverse Single Spin Asymmetry generated by the Sivers
effect. The crucial issue of the sign change of the Sivers function in lepton
pair production, with respect to Semi Inclusive Deep Inelastic Scattering
processes, can be solved. Predictions for the expected magnitude of the Single
Spin Asymmetry, which turns out to be large, are given.
