Go to the three-dot menu at the upper-right of Chrome to select Settings > Show advanced settings > Clear browsing data (or in the omnibar type "chrome://settings/clearBrowserData" without the quotation marks). This takes you directly to the dialog box to delete not only the history of your browsing, but also your download history (it won't delete the actual downloaded files), all your cookies, cached images and files (which help load pages faster when you revisit), saved passwords and more. Better yet, you can delete only the info from the last hour, day, week, month, or all of it to "the beginning of time."
Chrome doesn't give you the option to not collect your browser history, or set a window for how much it should hold. It just collects and collects until you go in and delete it.