New versions of Chrome automatically syncs your saved passwords to your Google Account.
Please access passwords.google.com to manage and see your saved passwords.
OLD CHROME VERSIONS:
Step 1) Copy the text below and Paste it into a New Tab in Chrome:
chrome://flags/#password-manager-reauthentication
Step 2) When you see "Disable Password Manager Reauthentication":
click Enable
Step 3)* Restart the computer.
* Step 3 can also be replaced with "Completely quit Chrome and Restart Chrome", or "Log Off Windows and Log On again" for those who know how to do so.
Credit: Solution found from googling "chrome asking for windows password", finding this thread and trying out their solution: https://productforums.google.com/forum/#!topic/chrome/DfyHFtf4zuw