How can I make such outlandish accusations? Well, have you run Caverns of Time: The Culling of Stratholme? At the very end, you'll see that Chromie's Dragon form sports a pretty thick beard. More importantly than that, Chromie's Draconic name is Chronormu. Following the naming scheme of the Bronze Dragonflight, names ending with -ormu are male, and -ormi are female. The exceptions being those ending with -os (male) and -a (female) which are general dragon naming schemes. Were Chromie indeed a female, her name would be Chronormi and not Chronormu.
Chromie is a man. A man, or a woman who had very cruel parents.