  The hydrodynamic limit of a one dimensional kinetic model describing
chemotaxis is investigated. The limit system is a conservation law coupled to
an elliptic problem for which the macroscopic velocity is possibly
discontinuous. Therefore, we need to work with measure-valued densities. After
recalling a blow-up result in finite time of regular solutions for the
hydrodynamic model, we establish a convergence result of the solutions of the
kinetic model towards solutions of a problem limit defined thanks to the flux.
Numerical simulations illustrate this convergence result.
