In Windows 7 and 8 Chrome store the browsing history at:
In Linux it is stored at:
In the default folder, there is a file called
History which contain the history information. The size of that file is the size of your stored history information. There might also be a file called
Archived History containing history information that predates the data in
History as well as per-month history files (e.g.,
History Index 2013-11).
There is, of course, also extra information in a lot of the other files, but these two are the primary ones and it is these two files that usually grow rather big (When we're talking history only).