We present a novel approach of identifying the Milky Way (MW) and Andromeda (M31) progenitors that could be visible as Lyman Alpha emitters (LAEs) at z∼ 6: we couple a snapshot from the Constrained Local UniversE Simulations (CLUES) project, which successfully reproduces the MW and M31 galaxies situated in their correct environment, to a LAE model. Exploring intergalactic medium (IGM) ionization states ranging from an almost neutral to a fully ionized one, we find that including (excluding) the effects of clustered sources the first Local Group progenitor appears as a LAE for a neutral hydrogen fraction (). This number increases to five progenitors each of the MW and M31 being visible as LAEs for ; the contribution from clustered sources is crucial in making many of the progenitors visible in the Lyα for all the ionization states considered. The stellar mass of the Local Group LAEs ranges between 107.2 and 108 M⊙, the dust mass is between 104.6 and 105.1 M⊙ and the colour excess E(B−V) = 0.03–0.048. We find that the number density of these LAEs is higher than that of general field LAEs (observed in cosmological volumes) by about two (one) orders of magnitude for (0.4). Detections of such high LAE number densities at z∼ 6 would be a clear signature of an overdense region that could evolve and resemble the Local Group volume at z= 0.