Step 1: Understand the question. We must pick the feature that is NOT a characteristic of chordates. Step 2: List the chordate features. Chordates show a notochord, a dorsal hollow nerve cord, pharyngeal gill slits, and a post-anal tail at some stage. Step 3: Check the post-anal tail. Presence of a post-anal tail is a true chordate feature, so this option is a real character. Step 4: Check the notochord and dorsal nerve cord. Presence of a notochord and a dorsal central nervous system are also genuine chordate features. Step 5: Check absence of gills. Pharyngeal gill slits are a defining chordate feature, so saying chordates show an absence of gills is wrong. Step 6: Conclude. Since the question asks for the feature that is NOT a chordate character, the answer is absence of gills. \[ \boxed{\text{Absence of gills}} \]
