  The chiral anomaly in lattice abelian gauge theory is investigated by
applying the geometric and topological method in noncommutative differential
geometry(NCDG). A new kind of double complex and descent equation are proposed
on infinite hypercubic lattice in arbitrary even dimensional Euclidean space,
in the framework of NCDG. Using the general solutions to proposed descent
equation, we derive the chiral anomaly in Abelian lattice gauge theory. The
topological origin of anomaly is nothing but the Chern classes in NCDG.
