Is it possible for a neuron to generate an action potential without stimuli?

Yes, it is possible for some neurons to generate an action potential without external stimuli. 

While sensory neurons require external stimuli to trigger action potentials, certain excitable cells can spontaneously depolarize their axon hillock and fire action potentials regularly, acting like an internal clock. These voltage traces are known as pacemaker potentials. An example of such cells is the cardiac pacemaker cells in the sinoatrial node of the heart. 

Although pacemaker potentials have a natural rhythm, their timing can be adjusted by external stimuli, such as signals from the sympathetic and parasympathetic nerves or pharmaceuticals. It’s important to note that these external stimuli do not cause repetitive firing. They only alter the timing of the firing.