Collective modes are the fingerprint of a condensed phase. The spectroscopy of these modes in superfluid He-3 and unconventional superconductors can provide key information on the symmetry of the condensate as well as the microscopic pairing mechanism responsible for the ground state and excitation energies. Here, we use interferometry within an acoustic cavity - which is very sensitive to changes in the velocity of transverse sound - to reveal a new collective mode in the B phase of superfluid He-3 (He-3-B). We identify the mode as an excited bound state of Cooper pairs, which is weakly bound with an excitation energy within 1% of the pair-breaking edge. On the basis of the selection rules for coupling of transverse sound to a collective mode in He-3-B, combined with the observation of acoustic birefringence near the collective mode frequency, we infer that the new mode is most likely a spin-triplet (S=1), f-wave pair exciton (orbital momentum L = 3) with total angular momentum, J = 4. The existence of a pair exciton with J = 4 suggests an attractive, subdominant, f-wave pairing interaction in liquid He-3.