We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3× T 2 by a ℤ N $$ {\mathrm{\mathbb{Z}}}_N $$ symmetry acting (possibly) non-geometrically on K3. We show that most of these models (in particular, for geometric symmetries) are self-dual under a weak-strong duality acting on the heterotic axio-dilaton modulus S by a “Fricke involution” S → −1 /NS . This is a novel symmetry of CHL models that lies outside of the standard S L 2 ℤ $$ \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right) $$ -symmetry of the parent theory, heterotic strings on T 6 . For self-dual models this implies that the lattice of purely electric charges is N -modular, i.e. isometric to its dual up to a rescaling of its quadratic form by N . We verify this prediction by determining the lattices of electric and magnetic charges in all relevant examples. We also calculate certain BPS-saturated couplings and verify that they are invariant under the Fricke S-duality. For CHL models that are not self-dual, the strong coupling limit is dual to type IIA compactified on T 6 / ℤ N $$ {T}^6/{\mathrm{\mathbb{Z}}}_N $$ , for some ℤ N $$ {\mathrm{\mathbb{Z}}}_N $$ -symmetry preserving half of the spacetime supersymmetries.