I have started to notice a new noise since having my timing chain replaced. It sounds just like radio hum and is coming from the right side of the engine. The sound increases up to about 2000-2200 rpm, after that it quiets down or I cannot hear over the engine. It is not a constant and seems more noticeable after driving for a few minutes. Could this be the water pump? Could this be normal? I am going to see what the dealer says about it on Monday. Thanks!
Edit: The noise is there when in park or drive, I don't believe it is the transmission.

 

I have a similar experience. I don't remember it being there prior to timing chain assembly replacement.

Mine sounds more like air in the coolant (gurgling sound). Did you get any resolution?

 

I had a mechanic check the car and he said that there are no problems with the car. I have not driven another Cooper S, so I cannot compare the engine sounds. It could be that I was paying too much attention to any sound from the chain that I never noticed the other noises.