Alan Cox, the quite well-known original main developer of the Linux kernel, did an implementation of Unix for the Z80:
https://plus.google.com/u/0/+AlanCoxLinux/posts/a2jAP7Pz1gj (https://plus.google.com/u/0/+AlanCoxLinux/posts/a2jAP7Pz1gj)
Here is the GitHub repro:
EtchedPixels/FUZIX · GitHub (https://github.com/EtchedPixels/FUZIX)
Cool thing is, that he choosed the Amstrad NC100 for the first supported real existing platform :)
EtchedPixels/FUZIX · GitHub (https://github.com/EtchedPixels/FUZIX#platforms)
There's already a thread FUZIX "Unix" for NC100 (and other Z80 systems soon) (http://goo.gl/IxzL9p)