The lithium-ion battery is currently the preferred power source for applications ranging from smart phones to electric vehicles. Imaging the chemical reactions governing its function as they happen, with nanoscale spatial resolution and chemical specificity, is a long-standing open problem. Here, we demonstrate operando spectrum imaging of a Li-ion battery anode over multiple charge-discharge cycles using electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM). Using ultrathin Li-ion cells, we acquire reference EELS spectra for the various constituents of the solid-electrolyte interphase (SEI) layer and then apply these "chemical fingerprints" to high-resolution, real-space mapping of the corresponding physical structures. We observe the growth of Li and LiH dendrites in the SEI and fingerprint the SEI itself. High spatial- and spectral-resolution operando imaging of the air-sensitive liquid chemistries of the Li-ion cell opens a direct route to understanding the complex, dynamic mechanisms that affect battery safety, capacity, and lifetime.