Update: MP4 (or more formally ISO BMFF) support is in Chrome Dev/Canary. You'll need to generate your MP4 files in a way that conforms to the Media Source spec. Fortunately, Media Source was written with MPEG-DASH in mind, so any DASH-compliant files will work with Media Source. GPAC/MP4Box is a great tool for this:
MP4Box -dash 5000 -frag 5000 -rap some_file.mp4
...will create 'some_file_dash.mp4', which should be compatible with Media Source. There are some bugs in earlier released versions of MP4Box, so I recommend building from SVN for now.
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