  The conormal Lagrangian $L_K$ of a knot $K$ in $\mathbb{R}^3$ is the
submanifold of the cotangent bundle $T^* \mathbb{R}^3$ consisting of covectors
along $K$ that annihilate tangent vectors to $K$. 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. 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
$T^* \mathbb{R}^3$ with boundary on $\mathbb{R}^3 \cup L_K$.
