The chord conjecture of Vladimir Arnold is a contact-geometry analogue of his well-known Lagrangian intersections conjecture in symplectic geometry.  It proposes that, for each Legendrian submanifold of a contact form on a compact manifold, there should be a integral curve of the Reeb vector field which crosses the Legendrian submanifold at least twice.  I will present the 2001 paper of Klaus Mohnke, which proves this conjecture for a class of compact contact manifolds including spheres.