Summary: We compare the hazard rate functions of the largest order statistic arising from independent heterogeneous gamma random variables and that arising from i.i.d. gamma random variables. Specifically, let \(X_{1},\dotsc ,X_{n}\) be independent gamma random variables with \(X_{i}\) having shape parameter \(0<r\leq 1\) and scale parameter \(\lambda _{i}, i=1,\dotsc ,n\). Denote by \(Y_{n:n}\) the largest order statistic arising from i.i.d. gamma random variables \(Y_{1},\dotsc ,Y_{n}\) with \(Y_{i}\) having shape parameter \(r\) and scale parameter \(\tilde{\lambda} = (\prod\nolimits_{i=1}^n \lambda_i)^{1/n}\), the geometric mean of the scale parameters \(\lambda_i\). It is shown that \(X_{n:n}\) is stochastically larger than \(Y_{n:n}\) in terms of hazard-rate order. The result derived here strengthens and generalizes some of the results known in the literature and leads to a sharp upper bound on the hazard rate function of the largest order statistic from heterogeneous gamma variables in terms of that of the largest order statistic from i.i.d. gamma variables. A numerical example is finally provided to illustrate the main result established here.