Yes, it is possible for rain to occur from a clear blue sky. This can happen when the air near the ground is warm and moist, while the air at higher altitudes is cooler and drier. The warm air can hold more moisture than the cold air, so when it rises, it can cause the water vapor to condense into clouds and eventually rain. This type of rain is often referred to as "virga" and it can occur even when there are no visible clouds in the sky.