Why do over 20% of children die in some poor countries, while in others only 2% die? We examine this question using survey data covering 278,000 children in 45 low-income countries. We find that parents' education and a mother's propensity to seek out modern healthcare are empirically important when explaining child survival, while the prevalence of common diseases, along with infrastructure such as improved water and sanitation, are not. Using a GINI coefficient we construct for treatment services, we find that public and private health systems are "equally unequal", that is, both tend to favor children in relatively well-off households, and neither appears superior at improving outcomes in very poor communities. These facts contrast with a common view that a much-expanded public health sector is necessary to reduce child mortality. Instead, we believe the empirical evidence points to the essential role of parents as advocates for their child's health. If we can provide better health knowledge and general education to parents, a private healthcare sector can arise to meet demand. We provide evidence that this alternative route to low mortality is indeed a reason behind the current success of many countries with low child mortality, including Vietnam, Indonesia, Egypt, and the Indian state of Kerala. Finally, we calculate a realistic package of interventions that target education, health knowledge and treatment seeking could reduce child mortality by 32%.