This will depend on how you're booting into elementary OS. Most of the solutions I found were specific to booting into OS X, so you might have more options if you still have OS X installed and/or are dual-booting. The startup chime should respect the latest software settings. I'd try the following:
- Mute the audio in OS X and see if the chime plays on reboot.
osascript -e 'set volume with output muted' in Terminal before exiting OS X and see if the chime plays on reboot, or whether it continues to play on reboot after only booting into elementary OS.
As far as I know, there is no easy way to touch that
osascript (AppleScript) functionality in Linux, but here is a lead if you want to hack around. If none of the above works, I'd attempt some commands from here or here, but do report back so we can find out what works!