First make sure you have good supplies in case the power goes out. If you experience tree falling either on or close to your house check for damage after it safe to venture outside.
Most masonry chimneys are relatively tough. If a falling tree makes a direct hit on your chimney that can in some cases help prevent major to your roof.
To make sure your chimney is still OK to use after such an event be sure to call your local NC Chimney Sweep Association member to come out and do a Level 2 inspection as needed..
A ” Level 2″ inspection involves the use of video camera in the chimney to check for cracks and gap in mortar that may have been caused by the sudden hitting event of the tree. Most of the time this is covered by Home Owners Insurance. One thing to consider if you have other damage be sure to include this service when the adjuster come out to access damage.
If you have no other damage I would be better to pay for this service your self and if damage is detected then file a claim on your HO insurance for the needed repairs. ( no need to file a needless claim)
If you chimney is a pre-fab type appliance the tree may have really damaged the chimney pipe and the surrounding wood structure as well. The damage can be evaluated and repairs can be preformed depending on age and condition of system. Older systems in a lot of cases are not repairable due to absence of replacement parts.
Talk with your chimney professional and insurance adjuster to see what may be the best course of action for your damage.