To clean morels: Cut off tough bottom of stem. Wash in 3 soaks of cold water. To first soak add 2 tablespoons salt and remove any wildlife that is drawn out.
Season chicken with salt and pepper. In a saute pan heat 1 tablespoon olive oil and add chicken breasts. To avoid crowding pan, chicken should be Sauteed in batches. Saute chicken until well browned on both sides and remove. Keep the sauteed chicken warm as you saute the rest. Keep all completed chicken warm as you proceed with morels.
To same saute pan, add remaining 1/2 tablespoon of olive oil. Add morels and saute for about 3 minutes. Add shallots and cook for 2 minutes. Add chicken back to pan. Add wine, cover and simmer for 3 minutes, until chicken is cooked through. Swirl in butter and serve.