We report, for the first time to the best of our knowledge, the discovery of quantized pulse separations between phase-locked soliton pairs in a thulium-doped fiber laser at the wavelength range of 2 μm. The soliton pairs are formed by the nonlinear binding interaction between the solitons and dispersive waves, and the two lowest-order Kelly sidebands drive the interaction in these soliton pairs and fix the pulse separations of the soliton pairs to a discrete set of values. Our experimental observations are well confirmed by numerical simulations.