For the sense of biting or chewing:
* Nourish: If something is gnawing at you, it's consuming you negatively. Nourishing suggests something positive that sustains you.
* Soothe: If something is gnawing at your stomach, soothing would be the opposite.
* Heal: If something is gnawing at a wound, healing would be the opposite.
For the sense of worrying or troubling:
* Reassure: If something is gnawing at your mind, reassuring would be the opposite.
* Comfort: If something is gnawing at your heart, comforting would be the opposite.
* Calm: If something is gnawing at your nerves, calming would be the opposite.
For the sense of gradual destruction:
* Build: If something is gnawing away at a structure, building would be the opposite.
* Strengthen: If something is gnawing at your resolve, strengthening would be the opposite.
* Preserve: If something is gnawing at your health, preserving it would be the opposite.
The best antonym for "gnaw" depends on the specific situation and what you're trying to convey.