  We prove a p-adic analogue of W\"ustholz's analytic subgroup theorem. We
apply this result to show that a curve embedded in its Jacobian intersects the
p-adic closure of the Mordell-Weil group transversely whenever the latter has
rank equal to 1. This allows us to give some theoretical justification to
Chabauty techniques applied to finding rational points on curves whose Jacobian
has Mordel-Weil group of rank 1.
