Have you called (pressed the OnStar button) and asked the advisor? After my '07 purchase, I was supposed to have 30 free min and when I tried to call someone, it told me I didn't have enough min to place the call. I called OnStar and they fixed it.
Additionally, OnStar and Verizon have a shared minutes agreement. I haven't started it, but I think you will pay to add an extra line to your Verizon account.
According to the Onstar.com website, the 2001 Tahoe is supposed to have it. The button to push for this function on your year is the white circle. My wife has a 2001 Suburban and the buttons are the same. If all else fails, press the blue button and the advisor will answer your questions or help you set it up.
I have logged onto my Onstar account on the website and purchased minutes there as well for my 2006 Silverado.
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