The (6)Pi-X (6)Delta band system of (FeCl)-Cl-35 near 357 nm has been recorded at 0.3 and 0.08 cm(-1) resolution by laser fluorescence excitation in a free-jet supersonic expansion of photolyzed Fe(CO)(5) diluted in seed gases containing CCl4. The (6)Pi(Omega' = Omega'-1)-X (6)Delta(Omega ") subbands for Omega(') = 7/2, 5/2, and 3/2 and upsilon' less than or equal to 4 of the Delta upsilon = 1, 0, -1, and -2 sequences were assigned, and excitation energies and rotational constants were derived for the relevant upper and lower vibronic levels. With the exception of the (0,0) band, for which one subband could be rotationally analyzed, it was not possible to assign any of the subbands with Omega' = 1/2, -1/2, or -3/2; these fine-structure components are expected to be strongly affected by homogeneous spin-orbit interactions with nearby sextet electronic states, leading to large Lambda doubling in the Omega' = 1/2 and -1/2 components. A subband with a large upper-state Lambda doubling was rotationally analyzed and assigned as the (6)Pi(1/2)-X (6)Delta(3/2) (0,0) subband. The effect of the off-diagonal spin-orbit interactions is discussed in light of the present results and previous theoretical work.