Step 1: Understanding the Concept
Brachiation is moving through trees by swinging from branch to branch with the arms, the body hanging below.
Step 2: The gibbon
Gibbons, the lesser apes, have very long arms, hook-like hands and flexible shoulder joints, which suit arm-swinging.
Step 3: Other apes
Chimpanzees and gorillas mostly knuckle-walk on the ground. The heavy orangutan climbs slowly using all four limbs.
Final Answer:
The gibbon is the brachiating ape.
\[ \boxed{\text{(C) }\text{Gibbon}} \]