Chimney removal isn't always complicated, but that doesn't mean you should attempt to remove the chimney yourself. Attempting a DIY chimney removal could lead to structural damage to your home or serious injury to you.
However, if you're committed to handling your chimney removal yourself, at the very least be sure to do your research and follow all the necessary safety precautions. For example, use safety equipment, like gloves, eye protection, dust mask, good work boots, and a safety harness to prevent you from slipping off the roof. Also, minimize dust and debris from getting into the house by hanging plastic sheeting around your work area.
Just like with any demolition, you'll likely need to get a permit before having your chimney removed. Generally speaking, the contractor handling the removal will take care of this. But if you're removing the chimney yourself, be sure to confirm with your local zoning laws whether or not you need a permit to do the work.