Preheat oven to 375F. Slice squash in half lengthwise and place cut side down on a cookie sheet. Bake until fork-tender and skin is starting to brown (about 30-40 minutes).
Once cool enough to handle, scoop out and discard seeds. Then scoop flesh away from skin and transfer to a blender, working in batches if necessary. Blend squash with broth as necessary to achieve a silky smooth soup consistency. Then blend in green chilies.
Reheat the soup on low on the stovetop if necessary. Season with salt and pepper if desired. Squeeze fresh lime juice over top before serving.