Not exclusively anymore - Samsung is starting to use it's own in-house chips for modems (some versions of S6 use them right now). Mediatek is doing the same I think. Intel has its own that the ZenFone 2 is using for example. Not sure about Apple.
Depends on what you mean by 'chips'— Qualcomm sells both discrete modems, which many cell manufacturers use, and systems-on-a-chip including modems, which they had recently been doing very well with, but just had a bad round of.
