Summary: Given a (finite or infinite) set \(X\), a collection \({\mathcal C}\subseteq {\mathcal P}(X)\) of subsets of \(X\) is called a hierarchy if it satisfies the condition “\(C_1,C_2\in {\mathcal C}\Rightarrow C_1\cap C_2\in \{\emptyset, C_1,C_2\}\).” In this note, we characterize maximal hierarchies as set systems that contain the empty set, the full set, and all one-element sets, and – in addition – satisfy either one of the following two requirements: (1) They are ample and finitary hierarchies, i.e. they are hierarchies that satisfy the two conditions (a) “\(C_1,C_2 \in{\mathcal C}\) and \(\#\{C\in {\mathcal C}\mid C_1 \subseteq C\subseteq C_2\} =2\Rightarrow C_2-C_1 \in{\mathcal C}\)” and (b) “\(\bigcup {\mathcal C}'\in {\mathcal C}\) as well as \(\bigcap{\mathcal C}'\in{\mathcal C}\) holds for every non-empty chain \({\mathcal C}'\) contained in \({\mathcal C}\).” (2) They are minimal among all ample and finitary set systems that contain the empty set, the full set, and all one-element sets.