I was plugging the power in, like I had hundreds of times before, and the chip at U36, right above the Edison, essentially turned into an ember and started smoking. I don't know what U36 is so I can't comment on what the root cause is, just be wary especially if you have a project that cycles the power.
According to the schematic, Here, U36 is a Micrel MIC2039 current limiting power switch, and it appears to only be used to supply power (5v, 0.5A) to the USB Host port.
Looks like it could have been caused by the lack of bypass capacitors (input and output) on the switch, and something bad happening with the switching supply on the board during power up, or a short somewhere near the USB Host port. The board should still work, though without USB host, though I can't be sure.