Multiscale wavelets are used to solve the quantum eigenvalue equations for the hydrogen molecular ion H-2(+) in the Born-Oppenheimer approximation. Normally restricted to Cartesian systems, "wavelets on the interval" (a normal wavelet family augmented by special edge functions) have recently been applied to such boundary value problems as the hydrogen atom in spherical polar coordinates [J. Mackey, J. L. Kinsey, and B. R. Johnson, J. Comp. Phys. 168, 356 (2001)]. These methods are extended here to ground and excited electronic states of the simplest molecule, for which the electronic Hamiltonian is separable in confocal elliptic coordinates. The set of curvilinear coordinate quantum systems for which wavelet bases have been applied is thus enlarged.