The conormal Lagrangian L K of a knot K in ℝ 3 is the submanifold of the cotangent bundle T * ℝ 3 consisting of covectors along K that annihilate tangent vectors to K. By intersecting with the unit cotangent bundle S * ℝ 3 , one obtains the unit conormal Λ K , and the Legendrian contact homology of Λ K is a knot invariant of K, known as knot contact homology. We define a version of string topology for strings in ℝ 3 ∪L K and prove that this is isomorphic in degree 0 to knot contact homology. The string topology perspective gives a topological derivation of the cord algebra (also isomorphic to degree 0 knot contact homology) and relates it to the knot group. Together with the isomorphism this gives a new proof that knot contact homology detects the unknot. Our techniques involve a detailed analysis of certain moduli spaces of holomorphic disks in T * ℝ 3 with boundary on ℝ 3 ∪L K .