AbstractFriction plays an essential role in most physical processes that we experience in our everyday life. Examples range from our ability to walk or swim, to setting boundaries of speed and fuel efficiency of moving vehicles. In magnetic systems, the displacement of chiral domain walls (DW) and skyrmions (SK) by Spin Orbit Torques (SOT), is also prone to friction. Chiral damping (α_c), the dissipative counterpart of the Dzyaloshinskii Moriya Interaction (DMI), plays a central role in these dynamics. Despite experimental observation, and numerous theoretical studies confirming its existence, the influence of chiral damping on DW and SK dynamics has remained elusive due to the difficulty of discriminating from DMI. Here we unveil the effect that α_c has on the flow motion of DWs and SKs driven by current and magnetic field. We use a static in-plane field to lift the chiral degeneracy. As the in-plane field is increased, the chiral asymmetry changes sign. When considered separately, neither DMI nor α_c can explain the sign reversal of the asymmetry, which we prove to be the result of their competing effects. Finally, numerical modelling unveils the non-linear nature of chiral dissipation and its critical role for the stabilization of moving SKs.