Abstract: The asymptotic group of symmetries of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to the Galilean Conformal Algebra (GCA) in 2d and a closely related non-relativistic algebra in 3d. The 2d GCA, obtained from a contraction of a linear combination of two copies of the Virasoro algebra, is generically non-unitary. The unitary subsector previously constructed had trivial correlation functions. We consider a representation obtained by the contraction of a different linear combination of the Virasoros, which is relevant to the relation with the BMS algebra in three dimensions. This is realised by a new space-time contraction of the parent algebra. This representation has a unitary sub-sector with interesting correlation functions. We discuss implications for the BMS/GCA correspondence and the consequences of this contraction in higher dimensions.