This paper studies the fixed-time output feedback stabilization control problem for chained nonholonomic systems. By means of switching control and $bi$-limit homogeneous techniques, it is firstly constructed two fixed-time state feedback stabilizing controllers for the considered systems. Then, a new state observer with a formalized switching law is proposed to fixed-time estimate system states, where high-order terms are applied to get uniform convergence regardless of initial conditions and low-order terms are aimed to the exact convergence in finite time. Finally, based on $bi$-limit homogeneous technique and Lyapunov stability theorem, fixed-time output feedback stabilizing controllers, one of which is discontinuous with a specific switching control law and the other is continuous, are constructed and the fixed-time output feedback stabilization of the considered systems is thus guaranteed. An example is presented to show the feasibility of the proposed fixed-time output feedback stabilization control strategy.