Forsythe (1957) has described a method for fitting polynomials to a set of points, using the principle of least squares. The method, designed to exploit the advantages of high-speed computers, uses orthogonal polynomials to overcome the problems of ill-conditioning which are usually associated with this approach. The present paper shows how this powerful method can be modified to save a substantial proportion of the machine storage. This is achieved by representing each polynomial within the machine by the coefficients in its Chebyshev series.