The 1g (3P1)-A (3)PI(1u) transition is analyzed by optical-optical double resonance using the 1g (3P1)-A (3)PI(1u)-X (1)SIGMA(g)+ photoexcitation sequence. The analysis of the 409 transitions in the upsilon' = 0-14 and J' = 2-51 range of Cl-35(2) isotope species yields a set of molecular parameters for the 1g (3P1) state in a Dunham-type expansion: Y00 = 59 295.651(5), Y10 = 256.6412(30), Y20 = -1.205 36(48), Y30 = 3.724(22) x 10(-3), Y01 = 0.114 313 8(60), Y11 = - 7.507(15) x 10(-4), Y21 = 1.96(13) x 10(-6), and Y02 = - 8.10(22) x 10(-8) with the OMEGA-type doubling constant, q(upsilon) = B(upsilon)(f) - B(upsilon)(e) = [3.176(31) - 0.0660(5) x (upsilon + 1/2)] x 10(-4) (all in cm-1 and sigma in parentheses). An empirical model is given to interpret the spin-orbit couplings between the nascent six ion-pair states of g-type symmetry correlating to Cl- (1S) + Cl+ (3P).