I noticed when you equip Starfire Protocol and the skill that gives you an extra grenade you can't have 3 grenades. Last time I looked the exotic chest doesn't grant you that exact skill so they should stack.
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Perks with the same effect don't stack. It doesn't have to be the exact description. For instance, field scout on a weapon (max ammo capacity) will not stack with extra ammo on armor for that weapon type.