A biexciton in a semiconductor quantum dot is a source of polarization-entangled photons with high potential for implementation in scalable systems. Several approaches for nonresonant, resonant, and quasiresonant biexciton preparation exist, but all have their own disadvantages; for instance, low fidelity, timing jitter, incoherence, or sensitivity to experimental parameters. We demonstrate a coherent and robust technique to generate a biexciton in an InGaAs quantum dot with a fidelity close to 1. The main concept is the application of rapid adiabatic passage to the ground-state-exciton-biexciton system. We reinforce our experimental results with simulations which include a microscopic coupling to phonons.