We examine the images of hundreds of planetary nebulae (PNe) and find that for about one in six PNe the morphology is too “messy” to be accounted for by models of stellar binary interaction. We speculate that interacting triple stellar systems shaped these PNe. In this preliminary study, we qualitatively classify PNe by one of four categories. (1) PNe that show no need for a tertiary star to account for their morphology. (2) PNe whose structure possesses a pronounced departure from axial-symmetry and/or mirror-symmetry. We classify these, according to our speculation, as “having a triple stellar progenitor.” (3) PNe whose morphology possesses departure from axial-symmetry and/or mirror-symmetry, but not as pronounced as in the previous class, and are classified as “likely shaped by triple stellar system.” (4) PNe with minor departure from axial-symmetry and/or mirror-symmetry that could have been also caused by an eccentric binary system or the interstellar medium. These are classified as “maybe shaped by a triple stellar system.” Given a weight η t = 1, η l = 0.67, and η m = 0.33 to classes 2, 3, and 4, respectively, we find that according to our assumption about 13%-21% of PNe have been shaped by triple stellar systems. Although in some evolutionary scenarios not all three stars survive the evolution, we encourage the search for a triple stellar systems at the center of some PNe.