I'm using Privoxy for this goal : you can add http auth header on each query, then use https://www.privoxy.org/user-manual/config.html#FORWARD to forward requests to the other proxy.
Then configure Chromium to use local privoxy instance.
For example, I suppose you have the following setup :
http_proxy=http://user:[email protected]:8080
Then, you can setup Privoxy to forward everything to your proxy :
forward / your.proxy.your.domain:8080
And add a custom filter in user.action file, to add http authentication header on each proxied request :
{{alias}}
proxy-auth = +add-header{Proxy-Authorization: Basic XXXXXXXX}
{ proxy-auth }
/
XXXXXX = login:password string base64 encoded
Finally, change http_proxy variable to use privoxy (without login/password, because they're added via filter) :
http_proxy=http://localhost:8118