  Non-relativistic versions of the AdS/CFT conjecture have recently been
investigated in some detail. These have primarily been in the context of the
Schrodinger symmetry group. Here we initiate a study based on a {\it different}
non-relativistic conformal symmetry: one obtained by a parametric contraction
of the relativistic conformal group. The resulting Galilean conformal symmetry
has the same number of generators as the relativistic symmetry group and thus
is different from the Schrodinger group (which has fewer). One of the
interesting features of the Galilean Conformal Algebra is that it admits an
extension to an {\it infinite} dimensional symmetry algebra (which can
potentially be dynamically realised). The latter contains a Virasoro-Kac-Moody
subalgebra. We comment on realisations of this extended symmetry in a boundary
field theory. We also propose a somewhat unusual geometric structure for the
bulk gravity dual to any realisation of this symmetry. This involves taking a
Newton-Cartan like limit of Einstein's equations in anti de Sitter space which
singles out an $AdS_2$ comprising of the time and radial direction. The
infinite dimensional Virasoro extension is identified with the asymptotic
isometries of this $AdS_2$.
