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Duke Eltan's Illness is a main quest that can be started in chapter seven, by hearing from Tamoko, Delthyr, or other potential sources that Duke Eltan has suspiciously fallen ill amidst Scar's assassination. Delthyr suggests following Eltan's healer Rashad, who reportedly leaves Flaming Fist Headquarters every night, but this cannot actually be done as there are no scripts allowing him to spawn outside the building.

Head directly into the Flaming Fist headquarters and kill anyone between the party and Duke Eltan. Alternatively, sneak in with a strong thief or someone strong and invisible. If you are hiding or invisible, you can avoid a fight with the enemy upstairs too. When you reach the second floor where Duke Eltan normally is, you find him and the man treating him, Rashad, who after a conversation turns out to be a greater doppelganger trying to kill the party. After he is killed, Duke Eltan will ask you to bring him to the Harbor Master, who is good friend of Eltan and can hide him from the loyal followers of Sarevok until he is recovered.

Now it's a good time to open to lockpick all containers there and see what kind of valuables are hidden, which includes a Medium Shield +1 and a Splint Mail +1.

When Eltan is brought to the Harbor Master, the latter will hide him and promise to take care of him. The party gains as a reward 2500 experience points and has probably done something good for the future of the city.