The short answer: In Chrome, press Shift+Esc to see what tabs are using up too much RAM, and refresh or reload those tabs from time to time to reclaim memory.
The long answer: I think this is more of a Chrome problem than a Ubuntu problem.
I recently ran into this problem using Windows 7 with a Chrome tab opened on rt.com with the comments section at the bottom of a story opened. The comments section is driven by spot.im and will consume over a gigabyte of RAM over an hour of doing nothing but sitting there. Windows 7 would issue a low RAM error and then I'd have to reboot. The same problem exists within Ubuntu + Chrome but not nearly as bad as Windows + Chrome.
Then I discovered Shift+Esc within Chrome to bring up memory display stats, where I could watch how much RAM each tab was consuming. This works on Windows and Ubuntu.
When available memory (RAM + SWAP) runs low, a program called "OOM Killer" (Out of Memory) starts up and "intelligently" kills running applications and stops new applications from running. OOM Killer was improved in Linux Kernel 4.6, but I can't say exactly how.
I did a test the other night using Chrome to burn up 95% of RAM and 65% of swap using OOM killer under Kernel 4.7.1 and the system remained stable. I couldn't do new things like Alt+Print Screen but could still reboot no problem. Chrome did error out on reboot and couldn't restore the 20 odd tabs from the previous session, but that isn't a surprise.