Magnetic systems are fertile ground for the emergence of exotic states(1) when the magnetic interactions cannot be satisfied simultaneously owing to the topology of the lattice - a situation known as geometrical frustration(2,3). Spinels, AB(2)O(4), can realize the most highly frustrated network of corner-sharing tetrahedra(1-3). Several novel states have been discovered in spinels, such as composite spin clusters(1) and novel charge-ordered states(4-6). Here, we use neutron and synchrotron X-ray scattering to characterize the fractional magnetization state of HgCr2O4 under an external magnetic field, H. When the field is applied in its Neel ground state, a phase transition occurs at H similar to 10 T at which each tetrahedron changes from a canted Neel state to a fractional spin state with the total spin, S-tet, of S/2 and the lattice undergoes an orthorhombic to cubic symmetry change. Our results provide the microscopic one-to-one correspondence between the spin state and the lattice distortion.