The Laser Interferometer Space Antenna (LISA) will detect gravitational wave (GW) signals from Extreme Mass Ratio Inspirals (EMRIs), where a small compact object -- a black hole, a neutron star, or something more exotic -- orbits a supermassive black hole and eventually plunges into it. By direct comparison of signals, we assess LISA's capability to detect whether the smaller compact object in an EMRI is endowed with a scalar field and to measure its scalar charge -- a dimensionless quantity that acts as a measure of how much scalar field the object carries. We show that LISA will be able to detect and measure scalar charge with an accuracy of the order of percent, which is an unprecedented level of precision. This result is oblivious to the origin of the scalar field and to the structure and other properties of the small compact object, so it can be seen as a generic assessment of LISA's capabilities to detect new fundamental fields.