I have a web application which acts as an interface to an offsite server which runs a very long task. The user enters information and hits submit and then chrome waits for
Let's assume:
This is not a server issue, so we don't have to go fiddle with Apache, nginx, etc. timeout settings.
The delay is minutes, not hours or days, just to make the scenario manageable.
You control the web page on which the user hits submit, and from which user interaction is managed.
If those obtain, I'd suggest not using a standard HTML form submission, but rather have the submit button kick off a JavaScript function to oversee processing. It would put up a "please be patient...this could take a little while" style message, then use jQuery.ajax, say, to call the long-time-taking server with a long timeout value. jQuery timeouts are measured in milliseconds, so 60000 = 60 seconds. If it's longer than that, increase your specified timeout accordingly. I have seen reports that not all clients will allow super-extra-long timeouts (e.g. Safari on iOS apparently has a 60-second limitation). But in general, this will give you a platform from which to manage the interactions (with your user, with the slow server) rather than being at the mercy of simple web form submission.
There are a few edge cases here to consider. The web server timeouts may indeed need to be adjusted upward (Apache defaults to 300 seconds aka 5 minutes, and nginx less, IIRC). Your client timeouts (on iOS, say) may have maximums too low for the delays you're seeing. Etc. Those cases would require either adjusting at the server, or adopting a different interaction strategy. But an AJAX-managed interaction is where I would start.