We present strong theoretical evidence that a Larkin-Ovchinnikov (LOFF/FFLO) pairing phase is favoured over the homogeneous superfluid and normal phases in three-dimensional unitary Fermi systems. Using a Density Functional Theory (DFT) based on the latest quantum Monte-Carlo calculations and experimental results, we show that this phase is competitive over a large region of the phase diagram. The oscillations in the number densities and pairing field have a substantial amplitude, and a period some 3 to 10 times the average interparticle separation. Within the DFT, the transition to a normal polarized Fermi liquid at large polarizations is smooth, while the transition to a fully-paired superfluid is abrupt.
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