Do you have any lockpicks??

@MasterGrater
When you go to unlock a chest, you will use a lockpick. If you succeed, you keep the lockpick to use next time, but if you fail, your lockpick will break. You will be unable to open a locked chest if you have no lockpicks in your backpack.

When you go to open a locked chest, you will enter a lockpicking screen. Here, you have 5 tumblers that must be set to the appropriate position. With the lockpick over one of the tumblers, press down your Left Mouse Button, or whatever the console equivalent is. Hold it down untIl the tumbler starts to wiggle and make a little clattering sound. If you hold for too long, the lockpicks will break. So be ready to release the button as soon as the tumbler starts shaking. Watch the very bottom of the tumbler. Do this for all 5 tumblers before time runs out to unlock the chest. The more difficult the chest is, the less time you will have before you will fail and have to restart.

Hope that answers your question.