Heat olive oil in large pot over medium-high heat until it begins to shimmer (about 1-2 minutes). Add diced onion and celery, and cook for 3-4 minutes. Add garlic and thyme, and cook for an additional 1-2 minutes. Do not let garlic brown.
Add flour, and slowly add milk and half and half, scraping the little brown bits from the bottom of the pot.
Add corn and simmer for 8-10 minutes until soft.
Add soup mixture to blender and pulse a few times until chunky (be careful with hot soup, and open blender vent and cover with towel, if possible).
Add soup mixture back to pot. Let simmer for additional 5-6 minutes. Add crab meat, and stir until combined. Serve immediately. Garnish with chives and drizzle with half and half.