This study uses data from the Early Childhood Longitudinal Study-Birth (ECLS-B) Cohort to estimate associations between two important indicators of family socioeconomic status--family income and maternal education--and children's school readiness measured by academic skills, behavior, and physical health at school entry. We find large gaps in our measures of school readiness across groups of children defined by family income and maternal education. Such differences are much smaller, however, when potential confounds are included as controls in regressions. In multivariate models, we find significant, but modest, links between household income and measures of children's achievement and behavior, but not health. Specifically, our estimates imply that an additional $1,000 of average income throughout early childhood would result in about a 0.015 standard deviation in reading and math scores for children in low-income families, with smaller effects in children's behaviors. With respect to maternal education, we find higher levels of education predict higher achievement and physical health, but not behavior. Our estimates imply that an additional year of school would increase math and reading scores by 0.06 to 0.09 standard deviations. The paper concludes with a discussion of the challenge of developing effective policies to increase family income and maternal education. Appended are: (1) School Readiness by Selected Non-SES Characteristics; (2) Regressions of School Readiness on Income: Full Results for Panel B of Table 3; (3) Regressions of School Readiness on Maternal Education: Full Results for Table 4, Panel C; and (4) Regression Results for Comprehensive Model that Includes Covariates that Are Themselves Predicted by Income or Education. (Contains 8 tables, 9 figures and 21 notes.)