Answer:
Yes. He was originally named Nick Chopper. He fell in love with the wicked witch of the east. But then he started to fall in in love with Glinda at Shiz, and the wicked witch of the east got jealous, and made his heart so small, it disappeared. Elphaba tried to save him, and made him into Tin.
But there is also another theory. Nick Chopper was in love with a slave of the wicked witch of the west, and she was afraid he would take the slave away, so she put a curse on his ax so that every time he used it, it would fall and cut a body part off of him. The tinsmith tried to help him and changed all his body parts to tin. He didn't have a heart, but went out searching for her, and forgot his oil can.