The elliptic Sombor index of a graph \( G \) with the edge set \( E(G) \) is a recently introduced degree-based topological index defined as \[ ESO(G)=\sum_{uv \in E(G)}\left(d(u)+d(v)\right)\sqrt{d(u)^2+d(v)^2}, \] where \( d_u \) denotes the degree of vertex \( u \).
In this paper, we present the ordering of the minimum elliptic Sombor index among all chemical trees, as well as chemical unicyclic, bicyclic, and tricyclic graphs.