I've not had any experiences with chalices, but I can give you two hypotheses that I have on that.
One, if you frag it with no eyes when it continues to grow they should appear; assuming the flesh has the zooxanthellae algae within it and not just on the eye, it would live.
Two, the eye is the location of the zooxanthellae algae and without it no photosynthesis could occur, thus killing the coral.
Also, I think chalices are lps corals. I know this didn't help at all, but maybe it will give you a way to search it better to find out for sure.