Though I bought my chilling carafe from a site other than Amazon, I was directed to it from the Amazon page for this product.
Though I read the several reviews (below) from people who broke the carafe the first time they tried using it, I figured hey, I can do better than that.
Well, I can't. I didn't break the carafe, but only because it immediately became apparent to me that the stainless steel chiller is TOO SMALL for the carafe, even if only by about 1/64 inch, so I didn't try forcing it on. It's obviously a defective match between the glass carafe and the metal chiller. There's a YouTube video showing how to use the unit, and it clearly shows the chiller being slipped into the carafe effortlessly. If you buy one of these and you can't do that, send it back, and DON'T try forcing the chiller into the carafe. There's obviously a defective batch of these units out on the market.
By the way, my thanks to reviewers Nate and Carlton. If it hadn't been for them, I'd have tried to force the chiller into the carafe and broken the glass.
Update as of 3 July: just got my replacement chilling carafe and it works fine: chilling unit fits snugly into the carafe, but there's no danger of it breaking the glass. Slides right in.