I’m sorry to hear about your chimney! Thankfully, your home insurance will cover your chimney damage.
Regardless of the type of homeowner’s policy you have, wind damage and falling objects are typically covered perils. Since the storm caused the tree branches to fall and damage your chimney, you can submit a claim to your insurance.
That said, most homeowner policies have deductibles. If the cost to repair your chimney is less than your deductible, you can’t submit a claim to cover the damage. If it’s more than your deductible, you can submit a claim. Once you pay your deductible, your insurance will cover the rest.