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By intersecting with the unit cotangent bundle $S^* \\mathbb{R}^3$, one obtains the unit conormal $\\Lambda_K$, and the Legendrian contact homology of $\\Lambda_K$ is a knot invariant of $K$, known as knot contact homology. We define a version of string topology for strings in $\\mathbb{R}^3 \\cup L_K$ and prove that this is isomorphic in degree 0 to knot contact homology. 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