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We perform Ramsey spectroscopy on the ground state of ultra-cold 87Rb atomsmagnetically trapped on a chip in the Knudsen regime. Field inhomogeneitiesover the sample should limit the 1/e contrast decay time to about 3 s, whiledecay times of 58 s are actually observed. We explain this surprising result bya spin self-rephasing mechanism induced by the identical spin rotation effectoriginating from particle indistinguishability. We propose a theory of thissynchronization mechanism and obtain good agreement with the experimentalobservations. The effect is general and susceptible to appear in other physicalsystems.

Spin self-rephasing and very long coherence times in a trapped atomic ensemble