When reading the title of this episode I was somewhat confused since I was not familiar with the word Queue other than a line of people. However during the first few minutes of the show when the Chinese man was seen getting off the stage there was no doubt where this show was going.
A Chinese man named Chen is on the stage that arrives in Dodge. When two cowboys see him getting off they make their way to him and throw him back inside the stage. They do not want no Chinese man in Dodge. Of course Marshal Dillon is a witnesses to the event and advises that any law-abiding person can live in Dodge and helps Chen make his way into town.
One evening Chen is threatened by the two cowboys and they cut his queue (pony-tail) off and tell him next time it will be his throat. When he still refuses to leave they basically hire a man for beer to go and take care of Chen. Bailey (Sebastian Cabot) goes over to where Chen is living with two goals. One was to make sure Chen leaves town and the other was to steal Chen's treasure box. One of the cowboys gives Bailey a gun to take care of business.
This is a story that is used many times in western plots. Just recently I watched a 'Rifleman' episode that had nearly the same exact plot. This was a way to give credence to race relations that was going on in the United States at the time. Sebastian Cabot was excellent as the shifty man that talked religious but was just a larger sinner than most. Even with suspicious plot the episode still played well. Good watch.