  A generally covariant extension of general relativity (GR) in which a
dynamical unit timelike vector field is coupled to the metric is studied in the
asymptotic weak field limit of spherically symmetric static solutions. The two
post-Newtonian parameters known as the Eddington-Robertson-Schiff parameters
are found to be identical to those in the case of pure GR, except for some
non-generic values of the coefficients in the Lagrangian.
