I prayed with the Messenger of Allah (may Allah's peace and blessings be upon him) and he placed his right hand above his left hand on his chest

"And he placed his right hand above his left hand."
The word 'hand', here, refers to the palm. This is supported by the Hadīth narrated by Abu Dawūd and An-Nasā’i in the following wording: "Then he placed his right hand above the surface of his left palm, along with the wrist and forearm."
"On his chest" means that he placed his right hand above his left hand and placed both of them on his chest while he was standing in prayer.