Wrong. There are some US banks offering Chip+PIN CREDIT cards. And some issuing Chip+Signature DEBIT cards. It all depends on which authentication methods the issuing bank coded into the card's chip, and which priority order they set them.
People saying "PIN is for Debit and signature is for credit" are taking anecdote as if it's industry-wide rule. Or are non-USAians who never knew how it works here.
The "Debit or Credit?" question that US Debit card users often are asked at Point of sale when making a purchase on a Debit card has nothing to do with whether it's a chip card or not, nor even whether it's a credit card or a debit card. It really means, "Process this like an ATM Bank card doing a checking account withdrawal? Which will require your ATM withdrawal PIN. Or, Process this like a credit card charge through the Visa (or MC) network, which will put a credit-card-style authorization on your account but not actually post the charge for hours or days?"
Not, "Is this a Debit card or a Credit Card?"
For the matter, you could always choose "Debit" with a real Credit card too, if you happened to know your "cash advance at ATM" PIN for your magstripe no-PIN credit card. Though most people didn't know that PIN, some Credit cards didn't have one unless you asked, and because at your credit card account it became a usually more-costly cash advance rather than a charge. But fundamentally, "Debit or Credit" is "act as if it's a bank ATM card or act as if it's a credit card", regardless of whether it's really a Credit IRS a Debit card.
"Act as if it's a bank ATM card" always required a PIN, ever since decades ago long before EMV chip cards reached USA.
"Act as if it's a credit card" never required a PIN, in USA.
What is new, and apparently confusing to Muricans, is that with EMV in most of the world, "Act as if it's a credit card" now also requires a PIN.
In USA, if your new EMV chip Credit card is done to world standards, "Act as if it's a credit card" does require a PIN, when in the past, "credit" never did. And too many US banks issued Chip+Signature (only, or Chip+Signature as priority 1 authentication method) cards, so that "credit" still would not require a PIN. Plus they even did the same for Debit Cards, so that when using the Debit card for a purchase as "act like a credit card" it does not use a PIN.
Which leads to confusion by cardholders and merchants alike, and the errors in so many of the posts here too.
My primary credit union's Visa Debit/ATM card requires the PIN for purchases even as "credit" if the POS terminal hardware, software, and merchant account are capable of following the card's EMV commands. Yet my other credit union issued Chip+Signature Debit MasterCard ATM cards. My bank issued a Chip+PIN priority Visa Debit, and the "checking alternative" account at my brokerage issued a Chip+Signature Visa Debit.
Of course all require a PIN when doing an actual ATM cash withdrawal. Or when doing a purchase through the "debit" ATM network.
I will stop now, before explaining how the Dodd-Frank Bill makes US-ussued chip Debit cards even more screwed up and globally non-standard even if they are true Chip+PIN. But it's all kinds of hilarity ensuing.