Place a heat-safe fondue pot or a medium-size saucepot over medium heat and melt the butter. Add the flour, let cook for a minute then add the mustard and whisk in the beer and chicken stock. Cook for a few minutes to thicken slightly.
Turn the heat down to medium-low and slowly add the cheese, stirring in a figure-eight motion. Remove from the heat and place on the platter with the dippers. Serve with fondue forks or long skewers.