  We give a proof of the formality conjecture of Kaledin and Lehn: on a complex
projective K3 surface, the DG algebra RHom(F,F) is formal for any sheaf F
polystable with respect to an ample line bundle. Our main tool is the
uniqueness of DG enhancement of the bounded derived category of coherent
sheaves. We also extend the formality result to derived objects that are
polystable with respect to a generic Bridgeland stability condition.
