Chaotic behavior and Stochastic Stability are two faces of the same RSB coin. In this talk I will discuss the universal properties of chaos against a small magnetic field in spin glasses. The introduction of a small field in a spin-glass modifies the weights of the equilibrium states. Using the fact that the magnetizations form a Gaussian process on the UM tree we can study the progressive decorrelation of the system in the field from the system without the field. We can then provide predictions on chaos that only depend on the Parisi function $P(q)$ in absence of the field. I will discuss in detail the simple case of the 1RSB, where extreme value statistics allow to completely solve the problem. In the full RSB case it is possible in principle to solve the problem through Parisi-like PDE, however, we found it more practical to simulate the infinite-system stochastic process implied by RSB theory. Getting a function $P(q)$ as input, we can generate weighted random trees using the Bolthausen-Snitman coalescent, reweight the states according to the values of their magnetization. We compare the theoretical predictions with direct simulations of Bethe-lattice spin glasses and the 4D Edwards-Anderson model. Work in collaboration with Miguel Aguilar-Janita, Victor Martin-Mayor, Javier Moreno-Gordo, Giorgio Parisi, Federico Ricci-Tersenghi, Juan J. Ruiz-Lorenzo