Heat oil in a large soup pot set over medium heat.
Add onion and salt; cook, stirring often, until onion is softened 5-10 minutes.
Add garlic, jalapeño, and chili powder; cook, stirring, 1 minute.
Add broth, tomatoes, chicken, and lime juice; stir to combine.
Bring to a simmer and cook, covered, until chicken breasts are cooked through, about 20 minutes.
Remove chicken from soup and shred with 2 forks.
Using an immersion blender, blend the soup until desired.
Return chicken to pot.
Serve soup garnished with cheese and tortilla chips. Serving size: 1 1/2 cup soup, 1 tbsp cheese, 2 tortilla chips