iDrive?
 

So I just went to the dealership for some work on the x, and noticed that in the new cars there is a pleasant "chime" sound when the door opens. On mine (an 04 x3), it's just a chirp :/

Is this an iDrive feature on the new models?

Yes, it comes on all the new F25 X3s, and pretty much all the new BMWs since 2008 in general even without iDrive.

Or you could be like me, and have the key chime just coded off altogether. Germans don't like errant warning chimes. They leave it for brainless Americans.