We prove existence of discrete solitons in infinite parity-time (PT-) symmetric lattices by means of analytical continuation from the anticontinuum limit. The energy balance between dissipation and gain implies that in the anticontinuum limit the sol
itons are constructed from elementary PT-symmetric blocks such as dimers, quadrimers, or more general oligomers. We consider in detail a chain of coupled dimers, analyze bifurcations of discrete solitons from the anticontinuum limit and show that the solitons are stable in a sufficiently large region of the lattice parameters. The generalization of the approach is illustrated on two examples of networks of quadrimers, for which stable discrete solitons are also found.
