In this paper, the Cˇerenkov radiation in an unbounded homogeneous isotropic chiral medium is studied and analyzed classically. Starting from the Maxwell equations and the proposed constitutive relations for isotropic chiral media, we formulate the problem for the electric and magnetic fields emitted from a charged particle moving with a constant speed in a chiral medium, and find a formal solution for the electromagnetic field components and energy spectral density of radiation. Notable features, such as double cone of propagation, and important characteristics of the Cˇerenkov radiation in such media in terms of the relative velocity of the particle with respect to the two characteristic phase velocities in the medium are discussed.