Legal Question in Real Estate Law in Illinois

Unfortunately, assuming you have a written lease, it is really impossible to say without looking at it. Most leases try to limit landlord responsibility for damages to tenant property unless there was actual negligence on the landlord's part. Assuming that is the case, proving the tree fell because of the landlord's negligence could be the biggest obstacle; while trees generally don't just fall over, high winds can topple trees that seem ok otherwise and so on top of the lease issue, you have factual issues. Even without a lease it would be prety much the same as a matter of law. A court could decide otherwise based on the facts, lack of them, but then we're talking a lawsuit.