Chess is a magical game, and there must always be unicorns hiding in the shadows. But i never heard of unicorns being carnivorous.
Unicorns

In the medieval tapestries at Cluny, the unicorn is often depicted
in a lush, peaceful garden, with contented little unworried rabbits and
loving maidens, so he probably has a diet similar to the horse.
Although he may get ravenous and plunder the corn!

Yes, it's true..... and, I was thinking, Ramona-Carbona, you never know, once in a while
they might be content with one cob of corn: hence,
be called Uni-corn?

I found a handpainted ceramic chess set at a flea market (only $5!) and was wondering about the origin of the pieces. It has not been fired yet, so the paint looks flat. The set looks older and I know it had to have taken someone a lot of time to paint each piece so detailed. I have never seen a set with a unicorn along with the knight. Ideas of where it may have originated from? Just curious. Can't wait to find a kiln to fire it. (attached is a pic of the knight and pawn) The knight is about 3"

Does anyone remember the unicorn song? The song tells that unicorns were not a myth, but a creature that literally missed the boat, not boarding the Ark in time to be saved from the Great Flood described in the Bible.

Bird would be a Phoenix, I'm guessing. If the rest of the set is fantasy-based. If it is medieval-based, then it is likely something non-fictional.
That's 'cause the unicorns ate the knights.