BNL-RHIC. We report the observation of transverse polarization-dependent azimuthal correlations in charged pion pair production with the STAR experiment in $p^\uparrow+p$ collisions at RHIC. These correlations directly probe quark transversity distributions. We measure signals in excess of five standard deviations at high transverse momenta, at high pseudorapidities eta>0.5, and for pair masses around the mass of the rho-meson. This is the first direct transversity measurement in p+p collisions. Comparing the results to data from lepton-nucleon scattering will test the universality of these spin-dependent quantities.