Nanoparticles, specifically magnetosomes, synthesized in nature by magnetotactic bacteria, are very promising to be usedin magnetic hyperthermia in cancer treatment. In this work, using the solution of the stochastic Landau–Lifshitz equation, we calculate the specific absorption rate (SAR) in an alternating (AC) magnetic field of assemblies of magnetosome chains depending on the particle size D, the distance between particles in a chain a, and the angle of the applied magnetic field with respect to the chain axis. The dependence of SAR on the a/D ratio is shown to have a bell-shaped form with a pronounced maximum. For a dilute oriented chain assembly with optimally chosen a/Dratio,a strong magneto-dipole interaction between the chain particles leads to an almost rectangular hysteresis loop, and to large SARvaluesin the order of 400–450 W/g at moderate frequencies f= 300 kHz and small magnetic field amplitudes H0 = 50–100 Oe. The maximum SAR value only weakly depends on the diameter of the nanoparticles and the length of the chain. However, a significant decrease in SAR occurs in a dense chain assembly due to the strong magneto-dipole interaction of nanoparticles of different chains.