Messages written via the logging macros in base/logging.h end up in different locations depending on Chrome's state:
/var/log/ui/ui.LATEST contains data written to stdout and stderr by Chrome (and technically also session_manager). This generally comprises messages that are written very early in Chrome's startup process, before logging has been initialized./var/log/chrome/chrome contains messages that are written before a user has logged in./home/chronos/user/log/chrome contains messages that are written while a user is logged in. Note that this path is within the user's encrypted home directory and is only accessible while the user is logged in.All of the above files are actually symlinks. Older log files can be found alongside them in the same directories.
Also notable is /var/log/messages. This file contains general syslog messages, but it also includes messages written by session_manager that may be useful in determining when or why Chrome started or stopped.
By default, only messages logged at severity WARNING or higher are written to disk. More concretely, LOG(INFO) messages are discarded.
When actively debugging issues, Chrome's --vmodule flag is sometimes used to temporarily log messages at lower severities for particular modules. See the Passing Chrome flags from session_manager document for more details, and specifically the /etc/chrome_dev.conf mechanism that can be used to change flags on development devices.