By parallel pumping experiments in ferromagnetic (CH3NH3)2CuCl4 chaotic auto-oscillations of magnon amplitude are observed at the pumping frequency of 9.39 GHz and the temperature of 1.65 K. Strange attractors constructed in three-dimensional phase space from time series data of chaotic oscillations display properties of stretching and folding of the sheet of trajectories. Fractal dimensions of strange attractors are obtained by the method of the correlation integral as a function of driving microwave power. With increasing driving power fractal dimension increases from 1.6 to 3.4. The largest Lyapunov exponent is obtained as $0.43\pm 0.05$ by using empirical return maps. The chaotic state arises directly from period-two oscillations without cascade of period doubling bifurcations.