The entanglement entropy of a single interval in 2d CFT is fixed by conformal invariance. This is generally not true for the entanglement entropy of multiple disjoint intervals. However, I will show that in any theory with a large central charge and a small number of light operators --- i.e. a theory that may plausibly have a holographic dual --- there is a universal formula for the entanglement entropy of multiple intervals. This is a (partial) CFT derivation of the Ryu-Takayanagi prescription for holographic entanglement entropy from the area of minimal surfaces. In the process I will discuss how 3d geometries arise very naturally in CFT calculations in this regime, without assuming holography.