Jamie Oliver owns several restaurant groups. The most famous is probably Fifteen, the restaurant in London that he opened and staffed, at least to begin with, entirely from young people who had dropped out of education and had no jobs. This was so successful that he has since opened two more 'Fifteen' restaurants, in Cornwall and Amsterdam. So that's three.
His biggest chain is Jamie's italian, which now has 32 outlets all over Britain. There is also Barbecoa, his new London steakhouse, and Union Jacks, specialising in British food, which has four outlets in the London area.
So as of December 2012 Jamie Oliver has 40 restaurants. However, he seems to be opening new ones all the time, so you can expect this figure to change regularly.
You can get full details of all the Oliver restaurants, their locations etc - plus new recipes if you fancy cooking some of the food yourself - here.