Fano resonances are features in absorption, scattering or transport spectra resulting from the interaction of discrete and continuum states. They have been observed in a variety of systems^,,,,,. Here, we report a many-body Fano resonance in bilayer graphene that is continuously tunable by means of electrical gating. Discrete phonons and continuous exciton (electron–hole pair) transitions are coupled by electron–phonon interactions, yielding a new hybrid phonon–exciton excited state. It may also be possible to control the phonon–exciton coupling with an optical field. This tunable phonon–exciton system could allow novel applications such as phonon lasers.