The problem cannot be solved.
Chris' statement is an if/then/otherwise statement that is missing the otherwise part. Under certain conditions he can be seen to be either telling the truth, telling a lie, or making a statement that has no bearing on the conversation.
Because the /otherwise part of the statement is missing and cannot be proved true or false, the other statements which are dependent on that cannot be proven.
What happens is a feedback loop where Tina is proved true, which proves Leonard true, which proves Chris a liar, which proves, Tina a liar, which proves Leonard a liar, which proves Chris true (about Leonard lying), which also proves Chris a liar at the same time(about Tina telling the truth), which proves Leonard true (about Chris telling the truth), which proves Tina true, which brings us back to steps 1 and 2. And so on and so on and so on.
Edit: Lets add the /otherwise statement. It has to be a statement unrelated to Leonard or Tina or Chris lying or telling the truth, because to do so would make another feedback loop.
Chris: If Leonard is lying, then Tina's telling the truth. Otherwise, Hydrogen is found on the periodic table.
Leonard: Chris or Tina - one of them is telling the truth.
Tina: Both Chris and Leonard are telling the truth.
In this instance the Tina is telling the truth, therefore Leonard is telling the truth, therefore Chris is telling the truth(if statement is proved false so otherwise statement is proved true). So all are telling the truth