Put onion and then potatoes in slow cooker. Add broth and 1 1/2 cups water. Cover and cook for 3 hours on high.
Coarsely mash potatoes; stir in corn, chicken, tomatoes and cream. Cover and let cook until heated through, about 10 minutes. (To make chowder ahead, prepare to this point, let cool, cover and chill for up to 3 days.) Season with pepper to taste.
Just before serving, stir oil, basil and salt. Drizzle basil oil over each serving.