© 2017 ACM.Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function f (x) defined on an interval [a, b] is ''rounded'' to a prescribed precision by constructing a Chebyshev series and chopping it at an appropriate point. Designing a chopping algorithm with the right properties proves to be a surprisingly complex and interesting problem.We describe the chopping algorithm introduced in Chebfun Version 5.3 in 2015 after many years of discussion and the considerations that led to this design.