The excitonic insulator is an intriguing electronic phase of condensed excitons. A prominent candidate is the small bandgap semiconductor Ta₂NiSe₅, in which excitons are believed to undergo a Bose-Einstein condensation-like transition. However, direct experimental evidence for the existence of a coherent condensate in this material is still missing. A direct fingerprint of such a state would be the observation of its collective modes, which are equivalent to the Higgs and Goldstone modes in superconductors. We report evidence for the existence of a coherent amplitude response in the excitonic insulator phase of Ta₂NiSe₅. Using nonlinear excitations with short laser pulses, we identify a phonon-coupled state of the condensate that can be understood as a novel amplitudemode. The condensate density contribution substantiates the picture of an electronically driven phase transition and characterizes the transient order parameter of the excitonic insulator as a function of temperature and excitation density.