Heat oil in a medium saucepan over medium heat. Add shallots, and cook, stirring occasionally, until shallots are translucent and tender, about 4 minutes. Add bell peppers and beets, and stir to coat. Add water and chicken stock, and bring to a boil. Cover partially, and reduce heat. Simmer until beets are tender when pierced with a knife, about 1 hour.
Remove saucepan from heat, and let cool slightly. Stir in lemon juice, and season with salt and pepper. Working in batches, puree mixture in a blender until smooth. Transfer to a large bowl, and refrigerate until chilled, up to overnight.
Divide soup evenly among 6 to 8 bowls. Sprinkle each with goat cheese. Season with pepper, and serve with lemon wedges.