Battery function is determined by the efficiency and reversibility of the electrochemical phase transformations at solid electrodes. The microscopic tools available to study the chemical states of matter with the required spatial resolution and chemical specificity are intrinsically limited when studying complex architectures by their reliance on two-dimensional projections of thick material. Here, we report the development of soft X-ray ptychographic tomography, which resolves chemical states in three dimensions at 11 nm spatial resolution. We study an ensemble of nano-plates of lithium iron phosphate extracted from a battery electrode at 50% state of charge. Using a set of nanoscale tomograms, we quantify the electrochemical state and resolve phase boundaries throughout the volume of individual nanoparticles. These observations reveal multiple reaction points, intra-particle heterogeneity, and size effects that highlight the importance of multi-dimensional analytical tools in providing novel insight to the design of the next generation of high-performance devices.