This issue was annoying me increasingly over the last few days. After googling around for a bit, I eventually found an answer that worked for me. Only step 4 is likely to be strictly necessary, but I did a bit of prep just to be sure I didn't break anything.
- Disabled my Internet adapter in the "Network and Sharing Center" under "Change adapter settings".
- Turned off my VPN program. (Most users won't have this).
- Ran "cmd" as administrator. You can do this by hitting the Windows key, typing "cmd" and then right-clicking on the "Command Prompt" search result and then click "Run as administrator".
- Inside the Command prompt, ran this command:
netsh interface ip delete destinationcache
- Turned my Internet adapter back on.
- Turned my VPN back on.
- Google Chrome is now fast again.
After a bit more investigation I realized that the problem was not solved. The fix that worked was using Google's public DNS servers (126.96.36.199 and 188.8.131.52) rather than the server that my network adapters were configured to use (probably related to my VPN). I made this update in the "Change adapter settings" view described above for each of my two network adapters. In each case, I clicked on the IPv4 settings and clicked "Properties". I then entered the above ip addresses as the DNS servers that I wanted to use. After this change, everything is back to full speed.