Typically when I'm dealing with JSON data, it's in the browser and I can use the handy JsonView Chrome extension, but in this particular instance it was a text file containing a string of json.
A quick google search led me to this blog post.
To format a file as json, run this command in Vim:
:%!python -m json.tool
Or, add this to your .vimrc, then select the bit of json and hit <mapleader>j.
map <Leader>j !python -m json.tool<CR>