In a large pot or Dutch oven, melt the butter over medium-heat. Add the squash, potato, salt and pepper, and saute for 3 minutes. Add the leek and saute an additional minute. Stir in the chicken broth, and return to a boil. Reduce the heat and cover the pot. Simmer until the potato and squash are tender, about 20 minutes.
Put half the mixture into a blender. Remove the center piece of the blender lid and cover with a kitchen towel. Blend until smooth. Pour into a large bowl. Repeat the process with the remaining soup. Pour back into the pot, then stir in the half and half. Let the soup warm through.
Divide the soup between 8 bowls. Top each with a sprinkle of bacon and chives.