A Boolean algebra is minimally generated iff it is the union of a continuous well-ordered chain of subalgebras, where each \(B_{\alpha +1}\) is minimally generated over \(B_{\alpha}\). This paper proves basic theorems about minimally generated algebras. For example: Theorem. Interval algebras and superatomic algebras are minimally generated. Theorem. Minimally generated algebras are closed under product, homomorphic image, and products of finitely many factors. Theorem. Every minimally generated algebra is co-absolute with an interval algebra. Theorem. A minimally generated algebra cannot have an uncountable free subalgebra.