Twin births are often construed as a natural experiment in the social and natural sciences on the premise that the occurrence of twins is quasi-random. We present new population-level evidence that challenges this premise. Using individual data for 17 million births in 72 countries, we demonstrate that indicators of mother's health and health-related behaviours are systematically positively associated with the probability of a twin birth. The estimated associations are sizeable, evident in richer and poorer countries, evident even among women who do not use IVF, and hold for numerous different measures of health. We discuss potential mechanisms, showing evidence that favours selective miscarriage. Positive selection of women into twinning implies that estimates of impacts of fertility on parental investments and on women's labour supply that use twin births to instrument fertility will tend to be downward biased. This is pertinent given the emerging consensus that these relationships are weak. Our findings also potentially challenge the external validity of studies that rely upon twin differences.