I am working my way through Lina Ng's theory book and I am stumped by a question which is 'draw a ring round the note which is chromatic to the key'. I haven't come across this before. The key is A major and there is a B sharp in the piece which I think is the right answer - but I really don't know. I would appreciate some help with this one.

Sounds right to me

Think of the notes in the key of A major
then see that B# is not part of that key.

Yes, I would say that's the correct answer too. I'm not a big fan of Lina Ng's books as I often find mistakes in them. There are many much better theory books available. Have you tried the Turnbull "Theory Time" books? They're fantastic!

That's right though I don't recall that wording being used on an AB theory paper.... could be wrong....
It is, as you worked out, a fancy way of asking which note doesn't appear in that key.