Here, we report an experimental realization of multimode strong coupling in cavity quantum electrodynamics. This novel regime is achieved when a single artificial atom is simultaneously strongly coupled to a large, but discrete, number of nondegenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. Our experiment reveals complex quantum multimode dynamics and spontaneous generation of quantum coherence, as evidenced by resonance fluorescence spanning many modes and ultranarrow linewidth emission. This work opens a new avenue for future experiments in light-matter interactions and poses a challenge to current theoretical approaches to its study.