Abstract. This article introduces interval Chebyshev interpolation, which incorporates the concept of interval inclusion into the well-known Chebyshev interpolation for highprecision function approximation, and provides a methodology for rigorous numerical computation. Based on the concept of numerical computation with Chebyshev interpolation, as introduced by the MATLAB toolbox Chebfun, we present three numerical results of rigorous numerical computation using the Julia language: quadrature, the error function, and finding the maximum and minimum values of a given function.