Pat the chicken thighs dry and season them generously with salt, pepper, and thyme.
Heat olive oil in a large skillet over medium-high heat until shimmering, then place the chicken thighs skin-side down.
Sear the chicken for about 4-5 minutes per side until golden and crispy, then remove from the skillet and set aside.
While the chicken cools slightly, chop the vegetables: slice carrots, celery, and dice the onion.
Add the chopped onion, carrots, and celery to the same skillet and cook for 3-4 minutes, stirring occasionally, until they start to soften and develop some color.
Pour the vegetables into the crockpot, then add the garlic, broth, and seared chicken thighs on top.
Cover the crockpot with the lid and cook on low for 6 hours, allowing the flavors to meld and the chicken to become tender and easy to shred.
Once cooked, remove the chicken thighs from the crockpot and shred the meat with two forks, discarding bones if present.
Return the shredded chicken to the crockpot and stir well to distribute the flavors evenly.
Taste the stew and adjust seasoning with additional salt, pepper, or herbs as desired.
Sprinkle chopped parsley over the top for fresh color and aroma, then serve hot with a side of paleo-friendly bread or on its own.