This item is similar in appearance to a doctor's bag. However, it is contaminated. With 35 Medicine, you can sterilize it with 1 bottle of either whiskey, scotch, or vodka (all of which can be found in a nearby fridge). Otherwise, you can replace the contaminated parts with 1 bottle of turpentine and 1 roll of duct tape, salvage it, or take it with you and sterilize it at a campfire. Note that salvaging the parts will give you less XP for the quest Tourist Trap than the other options.
It can be found on a table located in the back area of Zion Ranger station.
The Medical supply kit cannot be picked up, sterilized, salvaged, or interacted with in any way before the quest. Attempting to do so will simply pop up the usual notification that explains the kit's status, but with none of the options to interact with it displayed.