My guess is that it's the TIVO and not the TV, but it's just a guess. Here are a couple things to try. Hook up the TIVO with some other cables, either component or RCA (RCA will look bad, but it's just a temporary test). There could be some problem with the HDMI handshake that's causing it the freeze.
Try recording something on the TIVO and then play back the recording. There could be something messed up with the live-TV buffer that's causing it to freeze.
If you have any other input devices (DVD player, VCR, camcorder, etc.), it would be beneficial to hook them up temporarily to see if it's the TV or the TIVO (or a combination of the two). If you have another TV, you could try hooking the TIVO up to that.
Also, is just the TV new or the TIVO as well? Since you say that it's in the cable box, it's probably not actually a TIVO but is the cable company's DVR. If that's so and there's something wrong with it and not your TV, then you should be able to call their customer service and get them to ship you a replacement. We had to do this 2-3 times in the past with Dish Network DVRs.