Narrow-gap semiconductors are sought-after materials due to their potential for long-wavelength detectors, thermoelectrics, and more recently nontrivial topology. Here, we report the synthesis and characterization of a new family of narrow-gap semiconductors, R3Cd2As6 (R = La and Ce). Single-crystal X-ray diffraction at room temperature reveals that the As square nets distort and Cd vacancies order in a monoclinic superstructure. A putative charge-density ordered state sets in at 279 K in La3Cd2As6 and at 136 K in Ce3Cd2As6 and is accompanied by a substantial increase in the electrical resistivity in both compounds. The resistivity of the La member increases by 13 orders of magnitude on cooling, which points to a remarkably clean semiconducting ground state. Our results suggest that light square-net materials within an I4/mmm parent structure are promising clean narrow-gap semiconductors.