Bukkit

What is the enhancement in mind? How should it look and feel?

This feature should be configurable. If a player takes any damage, they cannot use the "/chest" command for "X" amount of seconds (configurable). If they try to use the command earlier than X seconds after taking any damage, the virtual chest window does not open, instead the player receives a message. Perhaps "You cannot use your virtual chest after taking damage."

Please provide any additional information below.

Players engaged in PVP combat will sometimes open their virtual chest when they are close to death and put some or all of their items into it, effectively keeping their items. We've made this against our server rules, but it is difficult to catch. So why not prevent it from happening to begin with?

Or to make it more general, maybe have a warmup time for the command. So when a player uses the command, X seconds go by until the virtual chest opens.

I believe this isn't AlphaChest's responsibility. You probably want a combat plugin to do this: https://dev.bukkit.org/projects/combatlog