We have analyzed a 1.2-ns molecular dynamics simulation of 51 mM d(CG.G)7 with 21 Na+ counter-ions and 1 M NaCl in water. Via the dipole fluctuations, the dielectric constant for the DNA is found to be around 16, whereas that for the bases and sugars combined is only 3. The dielectric constant for water in this system is 41, which is much smaller than 71 for pure SPC/E water, because of the strong restriction imposed on the motion of water molecules by the DNA and the ions. Also addressed in the present work are several technical issues related to the calculation of the dipole moment of an ionic solution from molecular dynamics simulations using periodic boundary conditions.