I'll stick my neck out and guess it's tissue from Booth's vertebrae
(sorry abou that)
I'll add a little more detail to Steve's answer.
"Thank you to the late Director of the Mütter Museum, Gretchen Worden, for clarifying the nature of the piece of John Wilkes Booth held by the museum. She indicated in a letter to me what was originally thought to be part of Booth's thorax is more likely to be tissue that was possibly cleaned off the cervical vertebrae. Her article entitled "Is It the Body of John Wilkes Booth?" in the December 1994 edition of Transactions & Studies of the College of Physicians of Philadelphia is an outstanding source of information regarding the topic of this web page."