Not all projectors have an HDMI in and there is no Mini Display/Thunderbolt port on Chromebook like there is on a Mac. Enter the Startech Display Adaptor. It is specifically designed to work with a Chromebook to convert the HDMI connection to VGA. I have no idea how this Digital to Analog conversion is done in such a small package, but I assume magic is involved in some sort or fashion.
Below is a video of me testing out this nifty piece of tech. I have no affiliation with Startech or Tiger Direct, I am just providing a public service announcement.