If you have the latest
Patch (1.47) Installed, you should be able to lockpick chests and barrels...
In act 1 you should be able to open almost every chest and barrel with level 3-5 lockpick. However, there are about 5 chests / barrels that you can only open with a key, since they are part of quests.
As Raze mentioned, i tend to carry all the stuff i cannot open to the Battlefields... and leave them there until i either leveled up in the skill or found the keys for them.
There are also a few doors (also quest / story line related) that you need a key / lever for ... but a lot of doors can be lockpicked.
