HTC Amaze was only recently announced however a developer on XDA by the name xboarder56has already come up with a simple 1 click root for all Amaze users. This is a permanent root and you will need an unlocked bootloader for this to work.

Rooting voids your warranty. Not following the instructionscarefullymight result in a bricked phone. Proceed at your own risk!

Instructions

Download and install HTC drivers from hereConnect your phone and turn USB debugging onDownload Easy Perm Root One Click from hereExtract to any location on your computerNavigate into Zerg rush folderClick ZergRushTempRoot.batWait like 3 minRebootEnjoy PermRooted Amaze 4g

For more details visit the original thread at XDA