The manner of bonding between constituent atoms or molecules invariably influences the properties of materials. Perhaps no material family is more emblematic of this than porous frameworks, wherein the namesake modes of connectivity give rise to discrete subclasses with unique collections of properties. However, established framework classes often display offsetting advantages and disadvantages for a given application. Thus, there exists no universally applicable material, and the discovery of alternative modes of framework connectivity is highly desirable. Here we show that chalcogen bonding, a subclass of σ-hole bonding, is a viable mode of connectivity in low-density porous frameworks. Crystallization studies with the triptycene tris(1,2,5-selenadiazole) molecular tecton reveal how chalcogen bonding can template high-energy lattice structures and how solvent conditions can be rationalized to obtain molecularly programmed porous chalcogen-bonded organic frameworks (ChOFs). These results provide the first evidence that σ-hole bonding can be used to advance the diversity of porous framework materials.