Chaotic current fuctuations have been observed in the negative differential conductivity region of n-GaAs at 4.2 K under static external conditions. Power spectra, Poincaré sections and the fractal dimension of the attractor were determined as functions of the applied voltage for various magnetic-field strengths B. For B = 0 only limit cycles were observed. For B > 0 our results indicate successive Hopf bifurcations and a Ruelle-Takens-Newhouse transition to chaos and point to a crucial role of the magnetic field.