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 × 102)–(3 × 104) 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) × 103 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.