A method for implementing the Incomplete Cholesky Conjugate Gradient algorithm on the CDC STAR-100 is described. The conjugate gradient method is used to solve the system of equations arising from the differencing of the elliptic partial differential equation (PDE) grad . D(x,y) grad u + cu = f(x,y). The method is implemented by use of a five-point difference approximation the PDE. The method is directly applicable to the nine-point case. 3 tables.