Chrome’s private browsing mode is called "Incognito." Chrome also lets you set a request that you not be tracked and provides the ability to control cookies and other tracking devices individually by site.
To turn on Private Browsing only for the current window, click the menu button at the top right corner of your browser window and choose "New Incognito Window."
Chrome does not provide a setting where you can make it always launch in Incognito mode.
Detailed information about Incognito browsing is available on Google’s Chrome support page.
Chrome’s privacy options are in the "Settings" dialogue box, which you can open from the menu button at the top right corner of your browser.
To access the privacy settings you have to scroll to the bottom of the regular settings and click "Show advanced settings." The detailed privacy settings are accessed by clicking the "Content Settings" button.
For more details see Google’s Chrome support pages.