We've found that a Chromebook may require that you have a powered HDMI to VGA converter rather than just a dongle to connect to an older VGA only projector or VGA monitor. Without the powered converter the Chromebook was not "detecting" that a HDMI cable was plugged in. Once the Chromebook "detects" the cable is plugged in (established when the Chromebook powers up) you can subsequently remove the power from the converter and it continues to function fine. This may not necessarily be an issue with all projectors.
We see that new projectors that are natively HDMI compatible do not have this issue.