This paper is devoted to the oscillatory properties of a third order neutral difference equation of the form \[ \Delta \left( c_n\Delta \left( d_n\Delta \left( y_n+p_ny_{n-k}\right) \right) \right) +q_nf\left( y_{n-m}\right) =e_n. \] Some sufficient conditions are obtained for oscillation of the solutions of the above equation. Existence of a nonoscillatory solution and its asymptotic behavior are also discussed. Examples illustrating the results are included.