Summary: Given \(f\in C[-1,1]\) and \(n\) points (nodes) in \([-1,1]\), the well-known Lagrange interpolation polynomial is the polynomial of minimum degree which agrees with \(f\) at each of the nodes. Properties of the Lebesgue function and Lebesgue constant associated with Lagrange interpolation on the Chebyshev nodes (the zeros of the \(n\)th Chebyshev polynomial of the first kind) have been studied by several authors. In this paper a study is made of Lagrange interpolation on the Chebyshev nodes augmented with \(-1\) and 1. It is shown that, although the convergence properties of interpolation polynomials based on the Chebyshev and augmented Chebyshev nodes are similar, there are considerable differences in the behaviour of the Lebesgue function. In particular, the local maxima of the Lebesgue function for the augmented nodes are strictly increasing from the outside towards the middle of \([-1,1]\), whereas they are decreasing for the unaugmented nodes, and the Lebesgue constant for the augmented nodes is essentially double that for the unaugmented nodes.