Speaking of Chicken, the original author has another implementation called Bones which is an r5rs that compiles directly to x86_64 machine code.
http://www.call-with-current-continuation.org/bones/
Another quite interesting implementation is Owl Lisp which is a "purely-functional" (in the sense of immutability; side-effects are still okay) subset of r7rs that ought to compile in pretty much any vaguely UNIX-y environment. It's full of clever tricks and has an eloquently-minimal vm and compiler-to-C. As an example of the clever tricks, it's got a system similar to erlang processes, IE closures with messageboxes, that you can use to simulate mutable state. There are some other immutable datastructure tricks to get efficient-enough, but conceptually much simpler under the hood, approximations of hashtables. Only thing is the documentation is essentially non-existent; you've got to look at the library source files. Still, it's fiendishly clever for how small and simple it is. A true embodiment of the minimal 'spirit' of Scheme.
https://gitlab.com/owl-lisp/owl