It does stain, but this is extrinsic stain (can be polished off)
natural tooth or porcelain.  If you have old acrylic facings, it MAY
stain permanently.
    For what it's worth, I generally feel a bit uncomfortable about
recommending Peridex for long-term use, not least because it is also
known to alter taste perception.

Steve

To keep staining down to a minimum, try and use Peridex when you're not
going to eat or drink staining foods/drinks for half an hour
afterwards. Usually the extrinsic stains can be removed. You may want
to schedule the cleaning earlier than usual though. You shouldn't use
Peridex continuously, but on a two-weeks on, two-weeks off basis,
because of its effects on soft tissues of your mouth.