Why such alias doesn't work? In my opinion there is problem with duplicated quotation marks.
New-Alias -Name "chrome" -Value ""C:\Program Files (x86)\Google\Chrome\Application\chrome.exe" --user-data-dir="%APPDATA%\Google\Chrome\User Data" --disk-cache-dir="%LocalAppData%\Google\Chrome\User Data""
To add to @boxdog's comment, pointing to the alias documentation, you must point your alias to a function if you want parameters.
Consider adding this to your
$profile
to accomplish your goal: