When grievance shocks have heavy tails, large sudden increases in grievances coordinate behavior far more effectively into protests than a sequence of small grievance shocks that generate the same final distribution of grievances in society. That is, society as a whole behaves like the legendary boiling frog, even though each individual does not. An implication is a strong form of path-dependence in collective action. To assess a society's potential for protest, it is not enough to know the current distribution of antiregime sentiments; we also need to know how they came about: suddenly or gradually. The theory also provides a rationale for the classic J-curve theory of revolution. We provide a quantitative analysis of the relationship between grievance shocks and protests in Chile in 2014-2019. Consistent with the theory, results suggest that, even after controlling for grievance levels, large grievance shocks increased the number of protests.