Unless something has changed recently, the Citi Executive card doesn't support Chip+PIN at all, only Chip+Signature (as is the case with most US-issued cards).
ON the other hand, basically all of the Barclay-issued cards support Chip+PIN as a fallback from Chip+Signature, so you could probably just get a different card from them to fill this gap (maybe something like the JetBlue card which seems to have no annual fee and no foreign transaction fees).