how do you find your iphone when its dead on a chrome book

If its dead, then you cannot find it in any way other than looking for it as you would any other thing.

If it were not dead, and still transmitting a signal, you could have logged into iCloud.com website on the Chromebook, and used the Find My iPhone App there to look for it.

But if its dead, its not transmitting anything, and its like looking for a brick, or a book.

For Find My iPhone to work, the following conditions must be met on the device:

• The phone must have been activated and registered to an AppleID.
• iCloud must be active (signed on).
• The Find My iPhone feature must be active in Settings / AppleID / iCloud / Find My iPhone.
• Location Services must be active.
• The phone must have some form of connectivity, cellular or Wi-Fi.
• The last two also imply the device has enough charge and is powered on.

If all the above are met, you can look for it either via the Find My iPhone app on another Apple mobile device or by logging on a browser into the AppleID/iCloud account the phone is registered to and using the Find My iPhone tab therein.