The shocking thing to me is that a timing chain needs service at 125k miles. I'm on my 5th BMW, two with the M50, two with the M52, and 1 with the M54 (the M54 is a recent acquisition) and I've never even considered that the timing chain needs attention.

One of my M50s, and both of the M52s, were(are) well into 200k miles. I have an M50 today that has 160k miles and I have no reason to think the timing chain needs attention.

What makes you think you need a timing chain?