Is it illegal to open a restaurant with the stolen recipes of another restaurant

Illegal is probably the wrong word, but the first restaurant may have a civil claim against the second for unfair competition and other torts.  It probably depends on whether the recipes are confidential enough to be considered trade secrets.  If the first restaurant's recipes were those found in the Betty Crocker cookbook, or otherwise in the public domain, they would probably not be considered trade secrets, but if they are unique to that restaurant, and the restaurant keeps them secret (for example, it doesn't publish them in a newsletter or cookbook), they may well be considered trade secrets which cannot be misappropriated.