Chrysoberyl is a mineral in its own right, not a beryl, despite the name; the two share beryllium and nothing else. Plain chrysoberyl is yellow to yellow-green, brilliant and tough, and cheap for what it offers. Its two famous varieties are alexandrite, which changes colour with the light and has its own article, and cat's eye, which this one is mostly about.
Cat's eye
Chrysoberyl with countless fine parallel tubes inside, cut as a cabochon with its base along those tubes, shows a sharp band of light that glides across the dome as the stone turns. Many stones can show a cat's eye, quartz and tourmaline among them, but "cat's eye" said without a mineral name means chrysoberyl, the sharpest and most valuable of them; the old name is cymophane. The best stones are honey-coloured to greenish yellow with a narrow, bright, straight eye that opens and closes as the stone tilts. A pale stone or a broad, blurry eye is worth less. Held under a single light with the eye across the stone, a fine one shows the "milk and honey" effect: one half of the dome milky, the other half honey, swapping as the light moves. Sri Lanka and Brazil are the classic sources. See optical effects.
What it is not
Quartz cat's eye and tiger's eye are the same effect in a softer, commoner stone at a fraction of the price; fibre-optic glass cat's eyes in bright colours are sold as tumbled stones and cost nothing. A jeweller's invoice should say "chrysoberyl cat's eye". Old "chrysolite" in Victorian jewellery is usually chrysoberyl, sometimes peridot; the name was used loosely, and misleading trade names attach to this stone more than most.
Wearing it
At 8.5 on the Mohs scale, chrysoberyl is harder than any stone except diamond, sapphire and ruby, and it has no cleavage to worry about. A cat's eye cabochon in a bezel is one of the most durable ring stones there is, and plain yellow chrysoberyl, faceted, is a bright and affordable alternative to yellow sapphire. See which stones can be worn every day. Describe your piece and a goldsmith can source the stone.