Are you playing champions that are eligible to earn a chest? If you have received a chest from a certain champion you can not get another from that same champion. Go into your champion page on your profile and look to see what champions are eligible to receive chests then go from there.
Follow up info from Riot's guide:
"Earn these through achieving a Mastery rank of S- or higher" - chests
"Once you earn a chest from achieving S rank on a champion, you won’t be able to earn another with that champion until the end of the season. You can see which champions you’ve earned chests with in your profile’s Champions tab. This chest cap resets each season."
"You can only earn chests if you're playing a champion you own. So, if you rent a champion or play an unowned champion on the free rotation, you won't be able to earn a chest with them."