Results of the first full-dimensional (6D) quantum calculations of the vibrational levels of the nu(1) and nu(2) HCl-stretch excited (HCl)(2), for total angular momentum J = 0, are presented. Three 6D potential energy surfaces (PESs) were employed. Two widely used PESs, the ab initio PES of Bunker and co-workers and the semiempirical PES by Elrod and Saykally, are found to give negligible tunneling splittings (less than or equal to 5x10(-2) cm(-1)) for the vibrational eigenstates of the nu(1)/nu(2) excited (HCl)(2), in sharp disagreement with the experimental tunneling splittings in the nu(1) and nu(2) fundamentals, -3.32 and 3.18 cm(-1). In an effort to overcome this problem, a 6D electrostatic interaction potential is constructed and added to the ES1 PES; the resulting 6D PES is denoted ES1-EL. Quantum 6D calculations on the ES1-EL PES yield greatly improved tunneling splittings for nu(1) (-2.31 cm(-1)) and nu(2) (2.45 cm(-1)), which are 70% and 77%, respectively, of the corresponding experimental values. The nu(1) and nu(2) fundamental HCl-stretching frequencies calculated on the ES1-EL PES are only 5.9 cm(-1) lower and 2.9 cm(-1) higher, respectively, than their experimental counterparts. In addition. the quantum 6D calculations on the ES1-EL PES provide a comprehensive characterization of the nu(1)/nu(2) supported vibrational eigenstates of (HCl)(2), including their energies, assignments, and tunneling splittings. The vibration-rotation-tunneling dynamics of (HCl)(2) in the nu(1) and nu(2) excited states which emerged from our calculations differs substantially from that observed for the HF-stretch excited (HF)(2).