Why do you think the chain has failed? Most likely cause of failure for these is the little plastic gear in the controller. This can be replaced for about $100; (seems like a lot for a little gear, but this is an aftermarket solution, and they clearly intend to make a good profit....but still way better than replacing the controller or the whole TC.)

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2014 BMW 328i Xdrive
2011 BMW 335i M-Sport
2008 BMW X5 4.8i Sport
2000 BMW 528i 5sp