Heat the olive oil in a large pot over medium heat. Add the ground turkey and cook, breaking it up with a spoon, until it is no longer pink.
Stir in the onion, carrots, and celery. Cook for 5 minutes until the vegetables begin to soften.
Add the garlic and cook for 1 minute more until fragrant.
Pour in the rinsed split peas, chicken broth, bay leaf, and thyme. Season with salt and black pepper.
Bring the soup to a boil, then reduce the heat to low. Cover and simmer for 45 to 50 minutes, stirring occasionally, until the split peas are very soft.
Remove the bay leaf before serving.