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In this paper we define and prove of the existence of the multi-point Green'sfunction for SLE - a normalized limit of the probability that an $SLE_{\kappa}$curve passes near to a pair of marked points in the interior of a domain. When$\kappa<8$ this probability is nontrivial, and an expression can be written interms two-sided radial SLE. One of the main components to our proof is arefinement of a bound first provided by Beffara [Ann. Probab. 36 (2008)1421-1452]. This work contains a proof of this bound independent from theoriginal.

Multi-point Green's functions for SLE and an estimate of Beffara