Good news, everyone! CodePen now supports Babel and JSX natively!
Include this file before the JSXTransformer in your external libraries in your JS Panel on Codepen.
Standard JSX Transformer rules apply (include your /** @jsx React.DOM */ comment at the top of the JS file).
I'm currently looking to prevent the 'Unexpected token <' when the JS first attempts to run so pull requests are welcome :)
For an example, check out this CodePen