DNS Overrider seems to be an extension that might do what you want, but reading the reviews and the details of it, I don't get a positive feeling towards it. However to set up a custom DNS server, you don't need to do it on your browser. You can set it on your operating system, and maybe that's why Google has decided to remove it from Chrome's settings.
Assuming you're on a Windows machine, you'll need to do this:
Control Panel > Network and Internet > Network and Sharing Center
Then from the left panel select "Change adapter settings".
A new window will open, listing you all the network connections that you have (i.e. Ethernet, WiFi, etc.).
Select the one you're using to connect to the Internet, and right click on it and select "Properties".
In the list from the opened dialog, scroll down to select either of these options depending on what IP version you're using (typically IP v.4):
Internet Protocol Version 6 (TCP/IPv6)
Internet Protocol Version 4 (TCP/IPv4)
Without unchecking the item, click on "Properties" button, and manipulate the DNS Server from the second section in this dialog:
And then confirm and save all the changes you've applied.
I always keep my DNS servers custom, which somewhat optimizing several factors. The addresses used in the screenshot are Open DNS addresses.