If on your summoner profile it says that you have 4 chests available, that means that you 4 open slots available to earn chests, not that you actually have them. In order to earn a chest, you need to get an S- grade or better on a champion.
Keep in mind that you can only earn one chest per champion per season, so once you earn a chest with a champion, you will be unable to earn another chest while playing as them until the next season. You can check which champions you have already earned a chest with by going to the champions tab in your summoner profile. Any champion with a special golden border is one that you have already earned a chest with, so you need to play a different champion to earn more.