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 solitons 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.