Black Cats

Yes. It would be extremely rare (not sure how it works). But I know of one such cat (mixed breed HHP) that was back in the 80's that was shown.

I was showing a mixed breed cat black/white bicolor who had a blue and a green eye. Another jealous exhibitor was determined to find something just as outstanding. She ran across a blue eyed black cat at a shelter and showed it for awhile.

I had a blue-eyed black as a kid, she was put together like a traditional Siamese, but as far as I know she was just your average moggie.

There are a couple of genetic possibilities that could result in a black cat with blue eyes but they are quite unusual.

The most likely scenario is that the cat was genetically a bicolour (black and white) but with no white visible on the body (the way white patches develop in foetuses carrying this gene is not that predictable and could potentially end up with a 100% black cat that is genetically bicolour, this is not the usual outcome but you could expect it to happen approximately 1 time out of 100,000 kitten births or thereabouts!), the white spotting gene that causes bicolours can affect the eyes and result in blue eyes. Blue eyed or odd eyed bicolours are not that unusual and are an expected outcome of bicolour x solid or bicolour x bicolour matings.