Chateaubriand refers to a recipe rather than a specific cut of beef. The recipe is said to be the creation of chef, Montmireil, for François-René de Chateaubriand (Vicomte de Chateaubriand) a dignitary who served as an ambassador to Napoleon. Yet another theory is that the dish was created by restaurant Champeaux after a book was published by Vicomte de Chateaubriand L'Itineraire de Paris a Jerusalam. (1811)
Today the dish is typically made from a thick center-cut of fillet, grilled, then served with a sauce bearnaise. The older version referenced above was cut from a thick sirloin and served with similar sauce made from white wine, shallots and a touch of demi-glace.
"A steak of superlative quality; it is cut in the fillet; it is particularly thick; it is broiled or grilled and served with pommes chateau and a sauce bearnaise" Wine and Food Society of London, 1947
Depending on what source you choose, the beef cut in the U.S. is the center portion of the beef tenderloin, serving 2 to 4 people. The diagram below is from Mastering the Art of French Cooking (Julia Child). The diagram shows the the cut being made next to the tenderloin butt on the rump/sirloin end. The balance of the center is used for filet steaks, next to that the smaller tournedos are cut and the filet mignon is the remaining few inches of the rib-end. Ms. Child defines the cut as the "tenderloin portion of a Choice or Prime porterhouse steak. It is cut 2 inches thick and should weigh a pound or more before trimming.
We have seen thick-cut sirloin steaks (roast) being sold at the local butcher under the name of Chateaubriand. If you can purchase a whole beef tenderloin at a reliable butcher (like Costco) you can cut the meat as you wish.
Here are some of beef cuts used for Chateaubriand. Either of these cuts can be substituted for one another: