If you are right in front a (double)chest (On floor height, NOT player height). You cannot open the chest.
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Confirmed on Asus B121 Tablet Touch & pen enabled, Win10 Pro (64-bit) build 10240, MCPE 0.13.0 in single player creative and survival.
The crosshair focus is on the block behind the chest (you can't see it but the chest is dark so it's not selected) when it should be on the chest. If you press and hold, you'll break (or interact with) the block behind the double chest (or behind & below the double chest if there's no block immediately behind it).
Confirmed on Asus B121 Tablet Touch & pen enabled, Win10 Pro (64-bit) build 10240, MCPE 0.13.0 in single player creative and survival.
The crosshair focus is on the block behind the chest (you can't see it but the chest is dark so it's not selected) when it should be on the chest. If you press and hold, you'll break (or interact with) the block behind the double chest (or behind & below the double chest if there's no block immediately behind it).