Structural, electronic and magnetic properties of the chromium (Cr) nanostructure formation on GaAs (1 1 1)-(2 x 2) surfaces are investigated. Studies are performed by first principles total energy calculations within the periodic spin polarized density functional theory plus Hubbard correction (GGA + U) with 1 < U < 5 eV, as developed in the PWscf code of the quantum ESPRESSO package. The chromium adsorption and incorporation into the GaAs(1 1 1)-(2 x 2) atomic structure are investigated on both gallium and arsenic terminated surfaces. Different coverage of Cr is considered from 1/4 monolayer (ML) up to a full ML to determine the relaxed configurations and the most favorable structure. High symmetry sites are considered to explore the Cr adsorption and incorporation into the GaAs structure, these are: H3, T4, Top and Bridge. Surface atomic structures contain different number of atoms therefore to determine the most stable atomic geometry the surface formation energies are constructed. On the As terminated surface, under As rich conditions the CrAs bilayer formation is the most favorable structure. On the Ga terminated surface, under Ga rich conditions the Cr trimer formation is the most favorable configuration. Electronic properties of the most stable structures are investigated by calculating the total density of states (DOS) and projected DOS. Results indicate that the most favorable nanostructures exhibit metallic behavior with antiferromagnetic characteristics.