I have to admit that I'd unknowingly collected two of the parts well before I even realised, or had heard of, the Chatterbox SMG!
If you don't know where to look, go to your Inventory, across to the materials/pouches section (the one that looks like a triple 9mm stick mag pouch) and scroll down to crafting materials section. Exotic materials use the diamond icon. There you can check what you have.
The parts drop from ANY Hyena box...except...one which you have to farm the Bank mission for (if I remember correctly).
The parts drop on ANY difficulty so you can run the missions on Normal, however, not invaded, as there's no Hyena boxes during invaded missions.
Sorry, think I made an error my blueprint advice. The first blueprint drops in the BANK HQ MISSION, but the UPGRADE blueprint is available from the vendor in the White House...however.. the Blueprint won't drop until you have all three parts either way, so my advise is still 50% correct.
Other ways to get the drops:
SMG Canister - Hyena boxes in Downtown East
SMG Creative Magazine - Hyena boxes in Federal Triangle
SMG Modified Mods - Hyena boxes in Judiciary Square
...no need to run any missions for these.
Basic blueprint (490GS) - Drops in Bank HQ mission, any difficulty level, non-invaded
Upgrade blueprint - available once you craft the 490GS SMG from White House vendor.
Drop rate (pre-todays patch) is pretty high, I only had an issue having to run Jefferson Trade Centre about 4 times for the magazine. The Blueprint dropped first time in the Bank HQ mission. I think the difficult issue for players will be if one of the missions in the area is Invaded, as that means you need to wait a whole week!
Hope the correction helps, sorry for my error before.