We extend the Brueckner-Hartree-Fock (BHF) approach by including the rearrangement contribution of a microscopic three-body force in calculating the single particle properties of nuclear matter. In the BHF approach, the TBF contribution is included by reducing the TBF to an equivalent effective two-body force V3eff. This effective force V3eff is density dependent. Due to the density dependence of the effective force V3eff, inclusion of the TBF in the BHF calculation may introduce an extra contribution UTBF to the single nu- We extend the Brueckner-Hartree-Fock (BHF) approach by including the rearrangement contribution of a microscopic three-body force in calculating the single particle properties of nuclear matter. In the BHF approach, the TBF contribution is included by reducing the TBF to an Due to the density dependence of the effective force V3eff, inclusion of the TBF in the BHF calculation may introduce an extra contribution UTBF to the single nu-