  Using {\sc Sphinx tt}, a new MC simulation program for transverse polarized
nucleon--nucleon scattering based on {\sc Pythia~5.6}, we calculate the
transverse double spin asymmetry $A^{TT}$ in the Drell-Yan process. If one
assumes (quite arbitrarily) that the transversity parton distribution $\delta
q(x,Q^2)$ equals the helicity distribution $\Delta q(x,Q^2)$ at some low
$Q_0^2$ scale, the resulting asymmetry is of order 1\%. In this case is
$A^{TT}$ would hardly be be measurable with PHENIX at RHIC.
