As a Warrior, you need to have a specific item in your inventory.
If you have no idea where to go...
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×Speak with the townsfolk about Fafnir and find where he might be hiding his chest.
If you haven't figured it out...
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×Enter the Crystal Cave in the southeast of the map.
If you can't figure out what to do there...
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×Enter the Crystal Cave with an intact Gram in your inventory.
If you damaged that item...
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×Do you know anyone who could repair a sword?
If you can't think of who that is...
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×USE the broken Gram on Volund and he'll tell you what he needs to fix it.
If you can't figure out where to get that item...
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×Coral drops from alf sorcerors randomly from a normal TOUCH action on the corpse.
So all at once:
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×If necessary, have Volund repair Gram with coral dropped by alf sorcerors. (You can then use it as a weapon.)
Ask the elf people about Fafnir, then head to the Crystal Caves in the southeast of the map with Gram in your inventory.
The rest will become clear then.
After you find the chest...
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×Don't give it back to Fafnir, unless you're a Rogue and can steal it back.
Warrior's solution:
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×Challenge and kill Fafnir in direct combat.
Everyone else's solution:
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×DO NOT challenge Fafnir (or else you can't leave until you kill him.) Run from him and throw the chest in the lake.
I don't know if the warrior solution is the "
most honorable"
way or not. Possibly it depends on whether or not you told Regin you refused to kill Fafnir.
I'm a warrior. 
