A monoclinic form of Fe3S4, a polymorph of cubic greigite, occurs as precipitates in a sample of pyrrhotite collected from the Sudbury ore deposit. The nano-crystal precipitates are in a topotaxial relationship with the host pyrrhotite-4C (Fe7S8). The precipitate and the host pyrrhotite have a coherent (001) interface. Half of the octahedral layers in the crystal structure are fully occupied by Fe, while the other half of the octahedral layers are occupied by Fe atoms and vacancies in an ordered manner along the a axis. The crystal structure of the Fe3S4 nano-precipitates has monoclinic symmetry with a space group of I2/m. Its c dimension is 6% smaller than that of the host pyrrhotite due to the large number of vacancies in the structure. Fractional coordinates for S and Fe atoms within the unit cell are determined from Z-contrast images and density functional theory (DFT). The calculated results match the measured values very well. It is proposed that the monoclinic Fe3S4 nano-precipitates formed through ordering of vacancies in pyrrhotite with a low Fe/S ratio (i.e. <0.875) at low temperature.