The USPTO suggests that recipes are best protected as trade secrets. http://www.uspto.gov/inventors/independent/eye/201306/ADVICE.jsp. Trade secrets normally require confidentiality agreements between the secret-holder and the recipient. Your question does not suggest such an agreement existed, so I cannot think of a legal mechanism by which the chef can limit his partner from using the receipes.
A different direction to consider, and this is outside my normal practice area, is business law. Specifically, partners are normally regarded as agents of each other with a fiduciary duty to each other. Business law in your area may see the chef from opening a new restaurant in the same market has his partner while leaving his partner behind and offering the same menu as his partner as a breach of fiduciary duty. For this aspect of your quesiton, I would speak to someone with more experience in business law.
The chef might be better served by taking the opposite approach and buying out his partner. This approach would be more expensive than moving down the street, but the added cost may be appropriate for the added value of not having a competitor offering the same menu and not having to worry about legal complications while starting a new venture.
Answered on Sep 11th, 2013 at 1:49 PM