Observation of a Skyrmionic spin texture in condensed matter systems began with quantum Hall ferromagnets. When the filling factor deviates slightly away from one (a single Landau level occupied with fully polarized spins), the excess amount of reversed spins spontaneously organize themselves into an intricate texture known as the Skyrmion. More recently, careful small-angle neutron diffraction studies on magnetic metals lacking inversion symmetry, such as MnSi and Fe1-xCoxSi, revealed a sixfold symmetric Bragg spots. The spots appear in the so-called A-phase in the phase diagram of these materials, where spin texture is now believed to be that of a

triangular crystalline array of Skyrmions. Motivated by such recent

advances in experiments, we present a theory of Skyrme crystal

formation in chiral magnets, which are ferromagnets with an additional

Dzyaloshinskii-Moriya interaction and a spiral magnetic ground state.

A new CP1 formulation of the Ginzburg-Landau energy for chiral magnets is shown to give a richer description of the possible complex magnetic phases than a conventional description based on O(3) non-linear sigma model order parameter. A phase diagram obtained from Monte Carlo simulation is presented that agrees nicely with recent experiments on magnetic thin films.