We propose and numerically demonstrate a new chiral spectroscopy method that is based on a universal system-independent mechanism of dynamical symmetry breaking in high harmonic generation (HHG). The proposed technique relies only on intense electric-dipole transitions and not on their interplay with magnetic dipole transitions. The symmetry breaking results in the emission of otherwise "forbidden" harmonics from chiral media (i.e., that are not emitted from achiral or racemic media), yielding a huge, nearly background-free, chiral-achiral signal that is correlated to the magnitude of the medium's enantiomeric excess. The handedness of the medium can be directly detected by measuring the polarization helicity of the emitted harmonics. Moreover, the strength of the "allowed" harmonics (that are not related to symmetry breaking) is chirality independent; hence, they can be used as a reference to probe chiral degrees of freedom within a single measurement. We numerically demonstrate up to 99% chiral-achiral signal level (normalized difference between the chiral and achiral HHG spectra) from microscopic gas-phase emission using state-of-the-art models for HHG in bromochlorofluoromethane and propylene oxide. We expect the new method to give rise to precise tabletop characterization of chiral media in the gas phase and for highly sensitive time-resolved probing of dynamical chiral processes with femtosecond-to-attosecond temporal resolution.