Is chimney an extraction thing or do you mean like a chimney above a stove? Oh duh you said fireplace. If it's on, don't ever do that no bad idea. If it's not on, theoretically yes, but there has to be a better place to do it. Chimneys are full of cancer causing creosote and other crap.
im with agentP', even if you are using good wood you cut/dried yourself, the chimney if full of tars and other nasty stuff you dont want to get around your weed
if you are interested in some alternative drying/ curing methods there is a really good thread about malawi style cob curing here
there is also another thread about a very interesting cure here as well, using controlled temperatures
/both filled with very good information and worth reading
Yes risky business indeed!
Got another idea, why not use the inline fan?
I mean, just connect an extra tube before the carbon filter and put the weed for drying there.
No smell and the airflow dry up the buds in no time!
I hang herbs to dry on the crane in my fireplace. I open the damper a crack and the warm air in the house drafts up through the chimney to the outside, creating nice airflow. Never hung any weed there but I imagine it would dry just fine.
edit: Fireplace is clean of any ash and unused this time of year, of course.