Many ARM-based chips include the "Jazelle DBX" (Direct Bytecode eXecution) hardware CPU extension, which lets "95% of [JVM] bytecode" be executed directly by the CPU -- without need for recompilation to 'native' ARM/Thumb instructions. (See http://en.wikipedia.org/wiki/Jazelle )
However, unlike most of the ARM universe which is fairly open, Jazelle DBX's specs, implementation, and operating details are apparently a closely held secret, shared by ARM only with select JVM implementors. I'll be interesting to see if ARM decides to help out the OpenJDK people. Googling around, it looks like so far the answer has been "No."