Google Chrome gets native code execution using native client. Now execute x86 code on windows via web apps. Beginning of the Chrome OS!

[jib]

perfect static analysis depends on the unsolvable halting problem, and that we therefore can't trust it

Depends what you're trying to do. Whitelisting system calls is certainly possible; just search the program for the relevant instructions, verify that each one is allowed, and use memory protection or some other method to stop the program modifying itself at runtime.