Two-photon photoassociation of colliding ultracold 7Li atoms is used to probe the Σu+3(a) ground state of 7Li2. The binding energy of the least-bound state of this triplet potential, υ=10, is found to be 12.47±0.04 GHz. This spectroscopic information establishes that the s-wave scattering length for 7Li atoms in the F=2, mF=2 state is (−27.3±0.8)a0. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.