This chapter describes routines for computing Chebyshev approximations to univariate functions. A Chebyshev approximation is a truncation of the series @math{f(x) = \sum c_n T_n(x)}, where the Chebyshev polynomials @math{T_n(x) = \cos(n \arccos x)} provide an orthogonal basis of polynomials on the interval @math{[-1,1]} with the weight function @c{$1 / \sqrt{1-x^2}$} @math{1 / \sqrt{1-x^2}}. The first few Chebyshev polynomials are, @math{T_0(x) = 1}, @math{T_1(x) = x}, @math{T_2(x) = 2 x^2 - 1}.