Yes google chrome uses a unique id to get "usage statistics" but that's if you enable it at the time of download or after downloading
the user id is located in a file named
Local State in
%USERPROFILE%\AppData\Local\Google\Chrome\User Data\ (Usually C:\Users\[USERNAME]\AppData\Local\Google\Chrome\User Data)
to see if google is collecting statistics open the Local state file using notepad and look for
client_id
here's a screenshot
To remove it click the wrench icon goto "options" and in the "Under the hood tab"
untick the "Help us make google chrome better" option.
Now the unique user id is gone