We prove that proper PAC learnability implies compression. Namely, if a concept C ⊆ ΣX is properly PAC learnable with d samples, then C has a sample compression scheme of size 2O(d). In particular, every boolean concept class with constant VC dimension has a sample compression scheme of constant size. This answers a question of Littlestone and Warmuth (1986). The proof uses an approximate minimax phenomenon for boolean matrices of low VC dimension.