Small-angle neutron scattering (SANS) on nuclei of chicken erythrocytes demonstrates the cubic dependence of the scattering intensity Q^{-3} in the range of momentum transfer Q∈10^{-3}-10^{-2}nm^{-1}. Independent spin-echo SANS measurements give the spin-echo function, which is well described by the exponential law in a range of sizes (3×10^{2})-(3×10^{4}) nm. Both experimental dependences reflect the nature of the structural organization of chromatin in the nucleus of a living cell, which corresponds to the correlation function γ(r)=ln(ξ/r) for r<ξ, where ξ=(3.69±0.07)×10^{3} nm, the size of the nucleus. It has the specific scaling property of the logarithmic fractal γ(r/a)=γ(r)+ln(a), i.e., the scaling down by a gives an additive constant to the correlation function, which distinguishes it from the mass fractal, which is characterized by multiplicative constant.