The loop O(n) model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin O(n) model. It has been predicted by Nienhuis that for 0\le n\le 2 the loop O(n) model exhibits a phase transition at a critical parameter x_c(n)=\tfrac{1}{\sqrt{2+\sqrt{2-n}}}. For 0 In this paper, we prove that for n\in [1,2] and x=x_c(n) the loop O(n) model exhibits macroscopic loops. This is the first instance in which a loop O(n) model with n\neq 1 is shown to exhibit such behaviour. A main tool in the proof is a new positive association (FKG) property shown to hold when n \ge 1 and 0
