The Trivers–Willard hypothesis (TWH) predicts that in a polygynous mating system, when fitness of male offspring is more variable than fitness of female offspring, mothers should invest more heavily in the sex with the highest marginal fitness returns. Females in good condition or high social rank should benefit by investing in sons, and females in poor condition or low social rank should benefit by investing in daughters. Many empirical studies have tested different aspects of the TWH, but no study has tested the assumptions and predictions in a single polygynous species using measures of maternal condition and maternal social rank, while accounting for random effects that can also influence offspring growth and survival. Here, we followed individuals in an isolated population of pronghorn on the National Bison Range, Montana, over multiple generations and tested the assumptions and predictions of the TWH. Pronghorn females who were in good condition or were socially dominant weaned larger fawns that were in better condition, but this advantage did not increase male fawn survival or reproductive success. We detected a slight bias in birth sex ratios according to maternal social rank, but overall we did not detect any adaptive benefit to mothers adopting a sex-biased investment strategy.