We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the d-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair of points x and y by an edge with probability , where is fixed and is a parameter, then the critical two-point function satisfies
for every pair of distinct points x and y. We deduce in particular that the model has mean-field critical behaviour when and does not have mean-field critical behaviour when .