* Chronic: This word does indeed contain a root related to time. It comes from the Greek word "chronos" meaning "time."
* Congenital: This word refers to something present at birth, but doesn't directly relate to a time root.
* Incorrigible: This word suggests someone who cannot be corrected, and doesn't have a time-related root.
* Notorious: This word implies being widely known, often for negative reasons, and doesn't have a time-related root.
Therefore, the only word from your list that contains a root meaning "time" is "chronic."