A new, exact, analytic approach to multivelocity, one-species, ballistic annihilation in one dimension is proposed. For an arbitrary one-particle initial velocity distribution, the problem can be solved rigorously in terms of the two-particle conditional probability, which obeys a closed nonlinear integro-differential equation. We present a method for solving this equation for an arbitrary discrete velocity distribution. This method is applied to the three-velocity case. The outcome of numerical simulations compares well with our exact results.