Electromagnetic surface waves supported by an isotropic chiral material were investigated via the associated canonical boundary-value problem. Specifically, two scenarios were considered: surface waves guided by the planar interface of an isotropic chiral material and (a) an isotropic dielectric (or plasmonic) material and (b) a uniaxial dielectric (or plasmonic) material. Both plasmonic and non-plasmonic achiral partnering materials were investigated. In scenario (a) surface waves akin to surface-plasmon-polariton (SPP) waves were excited, while in scenario (b) surface waves akin to Dyakonov waves and akin to SPP waves were excited. For numerical studies, an isotropic chiral material capable of simultaneously supporting attenuation and amplification of plane waves, depending upon circular polarization state, was used. The amplitude of the SPP-like waves could be either amplified or attenuated, depending upon the relative permittivity of the isotropic plasmonic partnering material for scenario (a), or depending upon the direction of propagation relative to the optic axis of the uniaxial plasmonic partnering material for scenario (b).