Development economics expects lower income inequality to improve food security by widening low-income households' economic access to the food basket. This paper tests that expectation for Iran. A structural vector autoregression with short-run recursive restrictions is estimated on annual data for 1983–2022, with oil rents, the size of the underground economy and economic growth as macroeconomic controls. A shock to the Gini coefficient has no statistically significant effect on the food security index at any horizon and accounts for a small share of its forecast error variance. Robustness checks show that the effect of inequality on food security is not significantly negative under any of the 24 possible orderings of the variables in the recursive identification, nor when the Gini coefficient is replaced by the ratio of tenth-decile to first-decile expenditure. The hypothesis that inequality reduces food security is therefore not supported by Iranian data. Descriptively, years in which the Gini fell were not, on average, years of improving food security; this co-movement survives controls for inflation but remains a reduced-form association that does not support causal inference. A simple formal model explains why: the Gini is invariant to the income level, and a fall in it is compatible with both a rise and a fall in the absolute purchasing power of the bottom deciles, so a stable link between the two variables should not be expected. The policy implication is that evaluating food security policy on the Gini coefficient alone can mislead; the measure should be reported alongside absolute indicators of food poverty among the lower deciles.