This is a Chrysler safety feature. It is done to enhance the turn signal by switching off the daytime running light. Hopefully oncoming traffic will see the turn signal more clearly as there are no other lights on.
I agree......................I thought this was odd too the first time I noticed it on my vehicle. But when I saw another Dodge approaching with their turn signal on and the headlight out, I thought it was pretty effective in highlighting the turn. Strange maybe, but I think it works well.