Magnetometry measurements in high quality LiFeAs single-crystals reveal a change in the sign of the magnetic hysteresis in the vicinity of the upper critical field $H_{c2}$, from a clear diamagnetic response dominated by the pinning of vortices, to a
considerably smaller net hysteretic response of opposite sign, which emph{disappears} at $H_{c2}$. If the diamagnetic response at high fields results from pinned vortices and associated screening super-currents, this sign change must result from currents circulating in the opposite sense, which give rise to a small field-dependent magnetic moment emph{below} $H_{c2}$. This behavior seems to be extremely sensitive to the sample quality or stoichiometry, as we have observed it only in a few fresh crystals, which also display the de Haas van Alphen-effect. We provide arguments against the surface superconductivity, the flux compression, and the random $pi$ junction scenarios, which have been previously put forward to explain a paramagnetic Meissner effect, below the lower critical field $H_{c1}$. The observed anomalous hysteresis at high fields will be compatible with the existence of chiral gap wave-functions, which possess a field dependent magnetic moment. Within a Landau-Ginzburg framework, we demonstrate how a $(d_{x^2 - y^2} + id_{xy})$ or a $(p_x+ip_y)$ chiral superconducting component can be stabilized in the mixed state of $s_{pm}$ superconductor, due to the combined effects of the magnetic field and the presence of competing pairing channels. The realization of a particular chiral pairing depends on the microscopic details of the strengths of the competing pairing channels.
