In chapter 2, the littlun with the mulberry-colored birthmark speaks up during an assembly. The littlun tells Piggy to ask Ralph what he is going to do about the "snake-thing." The littlun then refers to the enigmatic creature as a "beastie" and mentions that it is large and terrifying. Ralph and Jack respond by dismissing the littlun's fears and believe that he was simply having a nightmare. Ralph continually insists that there isn't a beastie before Jack grabs the conch to support Ralph's statement. Both characters do not believe that the littlun actually saw a creature and quickly dismiss the subject.

Ralph then addresses the need to create a signal fire so that passing ships will possibly rescue them. The boys then work together gathering firewood and use Piggy's glasses to spark the flames. Unfortunately, the fire erupts and spreads quickly throughout the forest full of dry, rotted wood, hence the title "Fire on the Mountain." The littlun with the mulberry-colored birthmark is lost in the burning forest and never seen again.  

In the novel "Lord of the Flies" by William Golding, the author shows us the idea of fear of a vague, shapeless kind. Then he shows us how the primeval fear present deep in the psyche of all of us, is given credibilty and even a name. The boys had a mixture of emotions when they were wrecked on the island - some would have been excited at the beautiful freedom of their surroundings but mixed in with that would have been fear of the unknown and of the removal of adult care. One of the first to articulate this fear is the littlun with the birthmark - he first calls it a "beastie." Ralph tries to be reassuring, but the only interest Jack has in the younger ones is as slavish little gang followers.Fire on the mountain refers to how the boys found a paradise and turned it into a scorched hell of their own evil.

What you are talking about happens in Chapter 2.  The littleun with the mulberry colored birthmark raises the question of the "beastie."  He says it's a snake-like thing and he is afraid of it.

Ralph tells him that there is no such thing.  But Jack starts talking about hunting it.

To me, the chapter is given this title because of what happens at the end.  The boys set the fire, but they are so careless that it gets to be a huge fire and it ends up killing the boy with the birthmark.