We present a neutron-scattering investigation of the crystal structure formed by pH -sensitive poly(2-vinylpyridine) microgel particles with 5 wt % of cross-linker. We focus on highly swollen particles and explore concentrations ranging from below close packing to well above close packing, where the particles are forced to shrink and/or interpenetrate. The crystal structure is found to be random hexagonal close packed, similar to the structure typically found in hard-sphere systems.