Abstract
We model discrete spatial solitons in a periodic nonlinear medium encompassing any degree of transverse nonlocality. Making a convenient reference to a widely used material--nematic liquid crystals--we derive a form of the discrete nonlinear Schrödinger equation and find a family of discrete solitons. Such self-localized solutions in optical lattices can exist with an arbitrary degree of imprinted chirp and have breathing character. We verify numerically that both local and nonlocal discrete light propagation and solitons can be observed in liquid crystalline arrays.