What is the most important thing that happened in Chapter 3 of Lord of the Flies?
In my opinion, the most important thing that happens in this chapter is actually two things. I think that what is important is A) Jack failing to kill the pig that he is hunting and B) Ralph and Simon failing to do a good job of building their hut. I think these are two related events -- they both show failure on the part of one of the leaders.
Because both of them have failed, they start to snipe at each other. They criticize each other for not being good leaders. This leads to some really bad blood between the two potential leaders. The enmity that starts to build here between Jack and Ralph is a major theme of the rest of the novel.