  We show that self-dual Nielsen Olesen (NO) vortices in $3$ dimensions give
rise to a class of exact solutions when coupled to Einstein Maxwell Dilaton
gravity obeying the Majumdar-Papapetrou(MP) relation between gravitational and
Maxwell couplings , provided certain Chern-Simons type interactions are
present. The metric may be solved for explicitly in terms of the NO vortex
function and is asymptotic to Euclidean space with signature (-1,-1,-1). The MP
electric field is long range but, strictly speaking, the charge of the vortices
is zero since the field dies off as $O(1/r (ln r)^2)$. The total ADM energy
integral of such vortices is {\it{zero}}.
  These peculiarities are due to the nature of the two dimensional Greens
function.
