Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Add oil, onions, celery, and bell peppers to the pot; saute until vegetables are soft, about 5 minutes.

Season chicken breasts with salt and , pepper and add to the pot. Add tomatoes, pearl barley, chicken stock, and thyme. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 25 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Remove chicken onto a cutting board and shred with 2 forks. Return to the pot and stir to combine.