In this talk, I would like to advertise the strict equality between two objects from very different areas of mathematical physics: - Kahane's Gaussian Multiplicative Chaos (GMC), which uses a log-correlated field as input and plays an important role in certain conformal field theories - A reference model in random matrices called the Circular Beta Ensemble (CBE) The goal is to give a precise theorem whose loose form is GMC = CBE. Although it was known that random matrices exhibit log-correlated features, such an exact correspondence is quite a surprise.