We study the transition from stability to chaos in a dynamic last passage percolation model on  with random weights at the vertices. Given an initial weight configuration at time 0, we perturb the model over time in such a way that the weight configuration at time t is obtained by resampling each weight independently with probability t. On the cube [0, ^n]d, we study geodesics, that is, weight-maximizing up-right paths from (0,0,⋯,0) to (n,n,⋯,n), and their passage time T. Under mild conditions on the weight distribution, we prove a phase transition between stability and chaos at t≍ Var(T). Indeed, as n grows large, for small values of t, the passage times at time 0 and time t are highly correlated, while for large values of t, the geodesics become almost disjoint.