0👍
✅
I had been defining React by including it on my html page:
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/0.13.0/react.js"></script>
What fixed the problem was requiring it instead in my .jsx file:
var React = require("react");
Not sure why this worked but from reading around, perhaps there were multiple initializations and/or definitions of React that were causing conflicts.
Thanks @Daniel for pointing me in the right direction.