In regular, casual speech you'd probably ask "Is there a table and chair?" If you asked "Is there a table and a chair?" it would sound very specific, as if you were emphasizing that you were seeking reassurance that both pieces of furniture will be available.Is there a table and chair?
Is there a table and a chair?
In this case, either is correct, and using the article in the second half of the sentence doesn't sound as stilted or unnatural as the previous example. When using the "or" conjunction it's not uncommon to include an article before each noun:Is there a table or chair?
Is there a table or a chair?
Game Show Host: "Do you choose the box or the curtain?"
Police Officer: "We can do this the easy way or the hard way."