Earlier this year LEGO conducted a trial in the Berlin and Bluewater brand stores, replacing plastic tubs with cardboard boxes for pick-a-brick purchases. Presumably it was deemed a success because they'll be appearing in all stores later this year, although we've not been informed exactly when.
A look at the Pick a Brick cardboard boxes
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Closer look at LEGO's new Pick-a-Brick packaging
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Cardboard boxes to replace tubs for Pick a Brick purchases