In gene, the giant DNA molecule forms a compact structure in the presence of oppositely charged histone proteins, through strong electrostatic interaction. The recent experiment has shown that while one histone protein binds with a giant DNA, this histone protein exhibits a greater probability to emerge at chain ends than in the middle of a DNA molecule. To better understand the electrostatic interaction involved in such a complex, a simple lattice model is developed. First, an ionic chain, consisting of identical charged monomers, is placed in the three-dimensional cubic lattice under the dilute solution without excess salt. To model the bound histone (wrapped up by DNA), one charged monomer in this ionic chain is substituted with a monomer unit of a different charge. The exact enumeration is then conducted to calculate all the possible chain conformations and to determine the thermodynamic stability of a given location of the bound histone in the model. Our finding shows that the net charge of a bound histone is essential to determine its stable position. For the bound histone containing the net charge opposite to chain monomers, the most stable location of the histone is in the middle of the ionic chain. While the net charge of the bound histone has the same sign as that of chain monomers, the histone becomes stable at near chain ends under appropriate conditions.