This paper offers an informal theory of fractal poverty traps that lead to chronic poverty at multiple scales of socio-spatial aggregation. Poverty traps result from nonlinear processes at individual, household, community, national and international scales that cause the coexistence of high and low equilibrium levels of productivity and income and high and low rates of economic growth. Multiple equilibria result from key threshold effects that exist at all scales due to market failures and nonmarket coordination problems. Key implications of fractal poverty traps include (i) the importance of recognizing meso-level phenomena in addition to conventional micro- and macro-level issues, (ii) inter-connections across social-spatial scales that foster or ameliorate chronic poverty, (iii) the importance of identifying and overcoming thresholds at which accumulation and productivity dynamics bifurcate, and (iv) the significant potential role of transitory donor and government interventions and safety nets to ignite sustainable growth among the poor.