We present results of experimental investigation of the chaotic and quasi-periodic regime in the chirped-pulsed (dissipative soliton) Cr:ZnS and Cr:ZnSe mid-IR oscillators with significant third-order dispersion. The instability develops when the spectrum edge approaches resonance with a linear wave either due to power increase or by dispersion adjustment. In practice, this occurs when the spectrum edge reaches zero dispersion wavelength. The analysis suggests a three-oscillator chaos model, which is confirmed by numerical simulations. The regime is long-term stable and can be easily overlooked in similar systems. We show that chaotic regime is accompanied by a characteristic spectral shape and can be reliably recognized by using wavelength-skewed filters and by second-harmonic or two-photon absorption detectors.