JSON Formatter provides buttons to toggle between raw and formatted views of a JSON document.
It is open source. As of November 2016, the last commit was in March 2015. There are over 100 forks, many of which have more recent commits. It's not immediately clear if one of those forks is better maintained.
The OP of this answer originally wrote: "I feel like a big dummy. Some more thorough searching turned up https://chrome.google.com/webstore/detail/the-missing-json-inspecto/hhffklcokfpbcajebmnpijpkaeadlgfn/related, which is exactly what I need." However, an edited version of this answer indicated that that extension was not open source and was no longer maintained.