Why was the founder of chess killed? I have heard from many a story in which a man who introduced the game of chess was hanged or killed by his king. What was the actual story and the the reason for killing the founder of chess?
The exact origins of chess are not known, but there are several stories about it out there. At the top of my head I can think of at least four different ones that I've heard myself, and after reading your question I suspect that you've heard of one such story about the creation of chess.

One of these, which may or may not be the story you seem to have learnt about, is the one that follows:

A long time ago, a bored king asked one of his underlings to bring him some form of fresh entertainment. The underling thought for a while, and came up with the game of chess. After playing one game, the king was so pleased with what the underling had brought him that he said that the underling could ask for anything he desired as a reward for the invention of the brilliant game. 

After contemplating for a while, the underling asked for a grain of rice for the first square of the chess board, two grains of rice for the second square, four grains for the third square, and so on for the remaining squares. The king agreed to the request, and when it was realized that the total amount of grains the underling had asked for was impossible for the kingdom to provide, the king got angry and ordered the execution of his underling for making a fool out of him.

It is important to note, however, that this story has no proven historical validity whatsoever.