Heat olive oil in a pot or large skillet over medium heat. Add the onion and cook for 3–4 minutes until softened.
Add garlic and cook for 30 seconds until fragrant.
Stir in chicken, white beans, cumin, chili powder, oregano, salt, and pepper.
Pour in chicken broth, starting with 1 cup and adding more as needed to create a slightly soupy chili mixture.
Bring to a gentle simmer and cook for 10–15 minutes, stirring occasionally, until flavors meld and the chili thickens slightly.
Warm the corn tortillas in a dry skillet, oven, or grill until pliable.
Spoon the white chicken chili mixture into each tortilla and top as desired.
Serve immediately with lime wedges for squeezing over the tacos.