We report the first measurement of the opening angle distribution between pairs of jets produced in high-energy collisions of transversely polarized protons. The measurement probes (Sivers) correlations between the transverse spin orientation of a proton and the transverse momentum directions of its partons. With both beams polarized, the wide pseudorapidity (-1≤η≤+2) coverage for jets permits separation of Sivers functions for the valence and sea regions. The resulting asymmetries are all consistent with zero and considerably smaller than S...