Layered delafossite-type compounds and related transition metal dichalcogenides, characterized by their triangular net structures, serve as prototypical systems for exploring the intricate interplay between crystal structure and magnetic behavior. Herein, we report on the discovery of the compound K_1-x CrSe₂ (x ≈ 0.13), an incommensurately modulated phase. Single crystals of this compound were grown for the first time using a K/Se self-flux. We find a monoclinic crystal structure with incommensurate modulation that can be rationalized by a 3 + 1-dimensional model. This modulation compensates for the under-stoichiometry of K cations, creating pronounced undulations in the CrSe₂ layers. Our anisotropic magnetization measurements reveal that K_1-x CrSe₂ undergoes a transition to a long-range magnetically ordered state below T _N = 133 K, a temperature 1.6 to 3.3 times higher than in earlier reported KCrSe₂ compounds. Our findings open new avenues for tuning the magnetic properties of these layered materials through structural modulation.