We present spectroscopic observation of an exceptional point or the transition point between mode crossing and avoided mode crossing of neighboring quasieigenmodes in a chaotic optical microcavity of a large size parameter. The transition to the avoided mode crossing was impeded until the degree of deformation exceeded a threshold deformation owing to the system's openness also enhanced by the shape deformation. As a result, a singular topology was observed around the exceptional point on the eigenfrequency surfaces, resulting in fundamental inconsistency in mode labeling.