How to deploy by stage with Chalice using CDK

I can't find any examples of how to deploy by stages (environments) when deploying a Chalice app with CDK, as spelled out here? https://aws.github.io/chalice/tutorials/cdk.html

I found https://aws.github.io/chalice/topics/stages.html, but can't find any reference to CDK.

What I want to do is deploy two different cloud formation stacks, pivoting by stage. I'd like a dev cf stack, as well as a prod stack. Each should have the same shape for their resources, but of course each resource should be distinct and namespaced according to stage.

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