Why build a Chalice/Athene's on Annie, you sure as hell don't need that much mana if you do it correctly. If you really want cdr, get a Morellonomicon and DFG. AD Annie is actually pretty fun and works pretty well. If her attack speed didn't suck as much as it does, it would probably see high level play on SR.
PS: Was replying to Jamial, but failed.
Chalice in ARAM is incredible, because ARAMS are all about poke. You won't get to sustain mana off your Q, since minions just die randomly most of the time (people aren't coordinated in Arams - also, the MR helps vs. magic dmg teams). I personally don't like DFG on Annie, since I don't feel it gives her what she needs, but I can see it working.