I don't think there's anything in the NEC that would preclude using this space. However, depending on how it's sealed, it might be considered a "damp" location, and require appropriate cabling and connections. I'd ask the local inspector before I took that route to the attic.

There may be an alternative that dodges the issue of breaking into the chimney, and the code issue. You may find that there is a space between the framing and the chimney brickwork where you can snake a wire. I've done that once. In another instance, the framing for the chimney was beefy and I was able to drill a hole without compromising the framing that allowed me to easily route the wire down from the attic.