This story took place during the warring states in the country of Qi. The leader of Qi was Qi Xuan Wang. We can call him King Qi for short. He enjoyed raising roosters for cock fights. Terrible sport, but that's because there were no street racing, boxing or other competitions for him back then.

He hired a cock-fighting expert named Ji Sheng Zi to train his pet roosters. But King Qi was an impatient dude so a few days after training began, he went to bother Ji Sheng Zi. The trainer said "No, this rooster is not ready."

King Qi returned a few days later to check on his roosters hoping that they'd be ready for fighting. He bothers Ji Sheng Zi again who responded, "This rooster is still not quite ready, he's easily angered and still needs more training."

King Qi's patience grew weary and he returned a few days later to ask the trainer. This time, he was surprised that Ji Sheng Zi said "Yes! This rooster is mature enough to fight!"

Finally, King Qi was able to bring his prized rooster to the fighting pits. 

Fighting between roosters is more than just aggressively attacking each other. There's also a mental aspect. You can't tell but the roosters are silently insulting each other and playing psychological mind games with each other. 

This particular rooster was so well-trained that he would maintain his composure no matter how much the opposing rooster would instigate it. King Qi's rooster would stay so still that it looked like a wooden chicken! The opposing roosters would stare at King Qi's chicken and be confused at its wood-like demeanor and all be too afraid to fight. That's how King Qi's rooster would go on to win numerous victories. Thus, the story behind "Dumb Like A Wooden Chicken."

Moral of the Idioms: Just because something looks dumb does not mean you should neglect its potential