  We establish an $h$-principle for exact Lagrangian embeddings with concave
Legendrian boundary. We prove, in particular, that in the complement of the
unit ball $B$ in the standard symplectic $\R^{2n}, 2n\geq 6$, there exists an
embedded Lagrangian $n$-disc transversely attached to $B$ along its Legendrian
boundary.
