Most US cards being issued with a chip are Chip and Signature, not Chip and PIN -- because banks have trained Americans to think PIN means debit so banks fear applying a PIN to a credit card would confuse people.
I have one of these Chip and Signature cards and on my last trip to UK it was a real PITA, especially at self-checkouts. Like at ASDA there was a signature signing pad but I had to wait for a clerk to come over to give me the pen and then she checked my signature real closely. Same thing at the duty free at the airport. The self-checking stopped and alerted the clerk to come over to check my signature. Then at other stores the clerk couldn't find a pen, or was surprised when paper spit out and had to ask a manager what was going on.
(I had one clerk hand me the slip to sign, checked my signature, then put the signed slip into the bag with the receipt! If I was an "arse" I probably could have disputed the charge and gotten away with it because they couldn't produce a signed slip)
At the ASDA (far away from where tourists usually go) the clerk remarked it's been years since she saw someone have to sign for a charge. I apologized, said I was an American, and that our banks think we are too stupid to remember a PIN. She got a good chuckle out of that...