This paper examines the link between political support for basic income funded by linear income taxation and income inequality by household and gender. We develop a model with an increasingly right-skewed distribution of skill across households and a gender wage gap within households. Household preference for basic income decreases as skill level increases and female labour supply decreases with time spent rearing children. Majority voting supports the basic income scheme as mean relative to median household skill increases. Household fertility and skill level are inversely related under the scheme. An increase in the marginal tax rate to fund required government revenue could exacerbate gender inequality by reducing female labour supply. Quantitative illustrations suggest that the recent peak in the mean to median wage gap would provide voting support for basic income from the majority of households in the United States. Basic income of $12,000 conditional on below-median wages would increase government spending by 10.8% which, if funded by progressive income taxation, could reduce the adverse effects on gender inequality.