Heat the olive oil in a pot on high heat. Add the onion, celery, garlic, and a pinch each of salt and pepper. Saute the veggies until softened. Add the flour and cook, stirring, 1 minute.
Add the chicken stock, scraping any browned bits from the bottom of the pot. Add the ginger, lemon zest, ham, and wild rice. Cover pot, reduce heat to low, and simmer 1 hour.
Add the cream with another pinch of salt, and cook, uncovered, another 30 minutes to thicken just a bit and blend flavors. Taste for seasoning, and add more salt as necessary. Serve with chopped chives sprinkled on top.