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A large class of systems of current interest (2D electron gases with spinorbit coupling, surface states of 3D topological insulators) can be classified as "chiral Fermi liquids", i.e., Fermi liquids with nontrivial correlations between electron momenta and spins. We extend the Fermiliquid (FL) theory to include spinorbit (SO) splitting of the energy bands, focusing on the Rashba SO coupling as an example. We construct the phenomenological Landau interaction function for such a system using the symmetry arguments and verify this construction by an explicit perturbative calculation. The Landau function is used to obtain the effective mass, compressibility, and stability conditions of the FL. It is shown that although the chargesector properties, such as the effective mass and compressibility, are determined solely by welldefined quasiparticles, the spinsector properties, such as the spin susceptibility, contain a contribution from damped states in between the spinsplit Fermi surfaces, and thus cannot be fully described by the FL theory, except for the case of weak SO coupling. We also show the chiral FLs support a new kind of collective modeschiral spin wavesand propose an experiment in which they can be observed. Host: Cristian Batista 