We live in Oregon and for over 20 years have rented a place that has a fireplace chimney. Occasionally, in the early winter evenings we will build a fire. We clean the fireplace on a regular basis. But we get tired of the Landlord asking us to clean the chimney at our expense every year. I would think that a Fireplace would be an tangible amenity, just like a dishwasher, refrigerator, stove, hot water heater and toilet. The landlord is responsible for keeping those amenities in safe working order; if they stop working the landlord by law has to repair them. So if a fireplace is part of an amenity, wouldn't the landlord be responsible for keep the chimney clean and fire safe so we can use it?
If your landlord is going to allow it's use, he could accept a copy of your bill from a chimney cleaning service twice yearly to assure it is properly cleaned. I would personally need to be present when being done, just like I am when a phone company, cable or satellite system is installed in one of my homes.
but that's just me.