Translation:The professor eats with the chairman.
"Vorsitzenden"... isn't that a plural form? Der Vorsitzende (one) --> die Vorsitzenden (many). So shouldn't be there "with the chairmen" instead of "with the chairman"?
there's a whole group of nouns where you have to add an "n" or "en" at the end http://www.vistawide.com/german/grammar/german_nouns03.htm
I heard "Der Professor ist mit dem Vorsitzenden". Is there anything wrong with this interpretation?
ist = is; isst = eats. In german, you never 'are with someone' (ist mit dem Vorsitzenden), but 'at someone' (bei jemandem, bei dem Vorsitzenden), so your interpretation doesn't work, since they're probably having a business-lunch somewhere.