With the use of recently computed diabatic potential energy surfaces (J. Chem. Phys. 2001, 115, 3085) a full ab initio calculation was made of the bound energy levels of the Cl(P-2)-HCl van der Waals complex for total angular momentum J = 1/2, 3/2, 5/2, and 7/2. The dissociation energy D-0 of the complex was found to be 337.8 cm(-1) for J = 1/2 and \Omega\ = 1/2, where Omega is the projection of J on the Cl-HCl bond axis. The complex is T-shaped in the ground state and in a series of stretch and bending excited states, with a van der Waals bond length R of similar to3.2 Angstrom. A series of states with linear geometry were also found, however, with \Omega\ = 3/2 and R approximate to 3.9 Angstrom, the lowest of which has a binding energy of 276.1 cm(-1). The rovibronic levels were analyzed with the help of one-dimensional calculations with R fixed at values ranging from 2.5 to 5.5 Angstrom and the use of diabatic and adiabatic potential energy surfaces that both include the important spin-orbit coupling. The states of linear geometry are in qualitative agreement with previous work based on more approximate potential energy surfaces; the T-shaped states of considerably lower energy were not predicted earlier. Analysis of the rotational structure and parity splitting of the rovibronic levels leads to the remarkable observation that this T-shaped complex shows several features typical of a linear open-shell molecule.