A new chemical entity (NCE) is, according to the U.S. Food and Drug Administration, a novel, small, chemical molecule drug that is undergoing clinical trials or has received a first approval (not a new use) by the FDA in any other application submitted under section 505(b) of the Federal Food, Drug, and Cosmetic Act.
A new molecular entity (NME) is a broader term that encompasses both an NCE or an NBE (New Biological Entity).