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Also known as Red Chalice after The Original Strife: Veteran Edition added the Blue Chalice to the game. The Red Chalice was found in MAP01: Sanctuary (Strife) behind glass and a force field which can be shutoff within the control room at the end of the map.

Ultimately the Red Chalice (aka Offering Chalice) is returned to Harris at the tavern who will make you return it to Governor Mourel.

SPOILER WARNING: Plot details follow.

If playing on the The Original Strife: Veteran Edition, you have nothing to fear. Go ahead and follow this quest line. However if on the original edition of the game, this leads to a Dead End, where you will be killed over time and have to start over. It is recommended to ignore the the chalice all together in this case.

Spoilers end here.