Abstract. The relative permittivity dyadic of a dielectric structurally chiral material (SCM) varies helicoidally along a fixed direction; in consequence, the SCM exhibits the circular Bragg phenomenon, which is the circular-polarization-selective reflection of light. The introduction of hyperbolicity in an SCM-by making either one or two but not all three eigenvalues of the relative permittivity dyadic acquire negative real parts-does not eliminate the circular Bragg phenomenon, but significantly alters the regime for its exhibition. Significantly wider circularpolarization-sensitive stopbands may be exhibited by hyperbolic SCMs in comparison to nonhyperbolic SCMs. Physical vapor deposition techniques appear to be suitable to fabricate hyperbolic SCMs. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.