You have a point in regards to the wording of “τῶν Χλόης.”  It is quite possible that its her family, those in her employ, or slaves that she owned.  All of those classes of people would fall into her household.  It is just not clear; all we can be sure of is that they are under her household. 

Thanks again for your input.

First, I think Chloe was a woman – but not everyone does (Much like the Junia discussion that I’m sure is forthcoming). If she’s not, as some contend, then this passage says nothing about women’s leadership.  Just thought I’d give you a heads up about what one objection might be.

Second, and this is more to your point, it is interesting to me that Paul says “those of Chloe.” He doesn’t appear to use that phraseology in any other instance. However, I think if we went with your interpretation (“those of Chloe” being other members/slaves of the community whom she leads) we run into a difficulty – namely that this is just simply an odd way of saying something that simple.   For my part, I’m much more inclined to read it as a reference to Chloe’s family (though, officially, if I recall right – slaves can be considered part of the household/family). Anyway, this understanding makes more sense to me simply because the possessive sense of the phrase resontates more clearly with household/familial circumstances – though, now that I think about it, possession certainly works with slaves as well!

That said, I still think your reading is great and either way – unless Chloe’s a man (which, between you and me, is a hard position to defend) she is certainly challenging cultural norms – whether in the family or in the larger Christian community!