Abstract: I will describe an algebraic construction that models the passage from a topological space to its free loop space, without imposing any restrictions on the underlying space. The input of the construction is a coalgebra over an arbitrary ring R equipped with additional structure and satisfying certain properties. The output is an R-chain complex equipped with a “rotation” operator. The construction is a modified version of the coHochschild complex of a conilpotent coalgebra and is invariant with respect to a notion of weak equivalence for coalgebras drawn from Koszul duality theory. When this construction is applied to a suitable model for the coalgebra of chains of an arbitrary simplicial set X, one obtains a chain complex that is quasi-isomorphic to the singular chains on the free loop space of the geometric realization of X. The construction is as small as it can be. Time permitting, we also discuss the relationship with Ed Brown’s twisted tensor product model in terms of the holonomy of the free loop space fibration given by the conjugation action of (a suitable model for) the based loop space on itself. This model for the free loop space is potentially useful in studying invariants arising in string topology of non-simply connected manifolds, some of which are able to distinguish homotopy equivalent non-homeomorphic manifolds.