ID a shell from Puerto Rico
This is the shell of a marine mollusk called a chiton.

They are also sometimes known as sea cradles or &quot;coat-of-mail shells&quot;, or more formally as loricates, polyplacophorans, and occasionally as polyplacophores.


In Puerto Rico, they call these animals &quot;Quitones.&quot;


All chitons bear a protective dorsal shell that is divided into eight articulating aragonite valves embedded in the tough muscular girdle that surrounds the chiton's body.

My initial guess as to the species is: Chiton tuberculatus.
 (Disclaimer: I know almost nothing about these animals, so this is at best a guess). 

 Source: NATURAL HISTORY MUSEUM ROTTERDAM 

 Source: NATURAL HISTORY MUSEUM ROTTERDAM 
You can find additional images that look even more like your specimen here and here
According to Wikipedia:

This species can be found under rocks and in spray zones of rocky shores, in the intertidal, shallow subtidal zone of Western Central Atlantic (USA, Colombia, Bermuda, Mexico, Venezuela and the West Indies)


This includes Puerto Rico

Based on Fig 1 of Crozier (1918) showing typical sizes of various ages of C. tuberculatus, you have a fairly young specimen (likely only a few years old).
The Quitones of Puerto Rico by Cedar García Ríos (ISBN: 1-932271-16-3) is probably a good tool for definitively IDing your specimen to species.