The chip is not part of the equation for online transactions. So if everything but the chip is stolen, the bad guys are going to use the card online.
Check out http://krebsonsecurity.com/2014/05/the-target-breach-by-the-..., particularly his "by the numbers" section:
0 – The number of customer cards that Chip-and-PIN-enabled terminals would have been able to stop the bad guys from stealing had Target put the technology in place prior to the breach (without end-to-end encryption of card data, the card numbers and expiration dates can still be stolen and used in online transactions).