Chewed bones are obtained exclusively as a drop from mithril dragons in the Ancient Cavern. No other monsters in the Ancient Cavern will drop chewed bones, and looting the skeletons won't give chewed bones either (only mangled bones).
When these bones are put on a pyre ship and burnt (requires a tinderbox, axe and any type of non-pyre log), they will summon a Barbarian spirit, who may thank you for putting his soul to rest with an item. The reward may be a dragon full helmet, various potions, runes or projectile ammunition. Many players will attempt killing mithril dragons in the hopes of obtaining a dragon full helmet drop; if unsuccessful, they can take any gained chewed bones to be burned in a pyre ship for another chance at gaining a dragon full helmet, however the chances of that are fairly rare. Note that using higher level logs does NOT increase chances of receiving a dragon full helm.
Burning chewed bones via a pyre ship provides an experience bonus (300%) to any bones buried for the next 5 bones. You will receive a message saying, "You gain extra prayer experience as the ancestral barbarian spirits watch over you." This bonus accumulates. Burning 2 chewed bones consecutively provides a bonus for burying twice as many bones as burning one chewed bone. Dying does not remove the accumulation of bonuses.
Monster Combat level Quantity Rarity Mithril dragon 304 1
Item Quantity Rarity GE market price Death rune 8–15 Common 1,760–3,300 Blood rune 4–27 Common 1,164–7,857 Diamond 2 Uncommon 4,058 Big bones 10 Rare 2,030 Dragon full helm 1 Rare (1/250) 39,128,592
Item Quantity Rarity GE market price Prayer mix(1) 1 Common 2,155 Prayer mix(2) 1 Common 4,837 Ranarr potion (unf)(noted) 2 Common 14,146 Anti-poison supermix(1) 1 Common 1,557 Super str. mix(1) 1 Common 1,431 Superattack mix(1) 1 Uncommon 1,743 Superattack mix(2) 1 Uncommon 653 Super def. mix(1) 1 Uncommon 432 Super def. mix(2) 1 Uncommon 735 Antifire mix(1) 1 Uncommon 451 Antifire mix(2) 1 Uncommon 842 Fishing mix(2) 1 Uncommon 119
Item Quantity Rarity GE market price Mith grapple 1; 2 Common 899–1,798 Silver bolts 5 Common 25 Rune arrow 10 Common 880 Rune dart(p) 20 Common 21,940 Rune knife 20 Uncommon 6,300 Adamant knife 20 Uncommon 8,020 Runite bolts 10 Uncommon 3,440