From the main menu, select System and open the Character Configuration menu, then select the Log Window Settings tab from the column on the left. Under the Log Details tab, check the box labeled "Add time stamp to messages." next to the desired chat channel.

The formatting of the time stamp can be adjusted under the General tab. The available time stamp settings allow you to select either local time or server time, as well as a 12-hour format or 24-hour format.