There's probably some obscure reasoning by which you can justify this statement (I think in this case they're meant to have sold the first chicken sandwich in a fast food restaurant) - but no, they're definitely not the first to put chicken between two slices of bread.

To take one counter-example, a quick search of google books leads to a passage in a book ("Society in India; by an Indian officer") published in 1841 with the sentence - "Having refreshed her guest... with a most unexceptionable cup of coffee and chicken sandwich" - clearly, these were not alien enough to warrant any special explanation in 1841.

This is the passage in question, by the way.