I hear you, sometimes that’s how you want to do things.
First and foremost you have to have a dns server on your local network. Sharing what particular software that is here might help others help you better. Software like BIND (on linux) or Dual DHCP DNS (on Windows) will do it.
Since I know too little about your environment, I can’t help more with the how, but eventually with a DNS server and hosts setup, and the client computer running Chrome pointing at this new DNS server (test it with either nslookup or ping) and the DNS will trnaslate those hosts to an ip address.
As another side point, if you just want a quick way to get the client running Chrome to see the domain and hosts locally, just edit the hosts file - it’s quick and dirty, but may help you work through the concept. This file is ususally located:
Windows: C:\Windows\System32\drivers\etc
Linux: /etc/hosts