We report on entering a new era of mid-IR femtosecond lasers based on amplification in a relatively new gain chalcogenide medium, Fe:ZnSe. Our hybrid all-solid-state laser system is based on direct pulse amplification of femtosecond seed from three-stage AGS-based-optical parametric amplification (OPA) in a Fe:ZnSe laser crystal optically pumped by a Cr:Yb:Ho:YSGG Q-switched nanosecond laser. The development of the pump source with output energy up to 90 mJ operating at a 10 Hz repetition rate regime and highly efficient grating compressor (80%) provides 3.5-mJ 150-fs femtosecond pulses centered at 4.4 μm. Diode-pumped Er:YAG/Er:YLF lasers make it possible to increase the beam quality and repetition rate of the proposed laser system up to 100 Hz. Focusing such a laser radiation into the ∼3λ beam diameter allows us to reach a focus laser intensity up to 1016 W/cm2 which is only an order of magnitude lower than a relativistic intensity of 1017 W/cm2 and enough to drive strong nonlinear optics in mid-IR. We show as a proof-of-principle experiment the generation of four-octave spanning (from 350 nm up to 5.5 μm) supercontinuum in xenon.