We obtain exact ground states for the spinless Falicov-Kimball model with hybridization in one dimension (d=1). Ground-state energies and their corresponding wave functions are given for a restricted region of the parameter space in the limit of strong interactions for the half-filling condition. We find that the ground states possess a diagonal long range order and constitute a condensation of excitons in a zero momentum state. On the other hand, the correlation function A = is purely imaginary, indicating that the ground state does not exhibit spontaneous ferroelectricity.