This is probably the greatest single source of parental tension in children older than toddlers. Adolescents, particularly, have entered a new phase of life where things are changing so fast for them physically and socially that they are tired (especially in the morning) and distracted. Family life may feel annoying and irrelevant to them, particularly where rules, chores, and nagging are concerned.
I've found that if we really leave room for kids to express their feelings and perceived needs, really hear them with sympathy, kids discover that they feel less reluctant to participate. They know Mom or Dad really cares about their experience.
So I'd find an opportunity to sit with her and say something like, "You know, sweetie, I've been remembering how hard it was when I was your age to care about my chores. Would you tell me how you feel when you're vacuuming, what you're thinking you'd rather be doing?"
After hearing and repeating her main thoughts back to her (shows you've really listened), you might follow with, "Wow, yeah, I still feel like that sometimes. Wouldn't it be great if the chores would just go away and nobody had to do them? Sometimes I wish I had the time or energy to do it all myself, but I'll tell you, I know I would resent that. Since you and Dad (and siblings?) all get to take advantage of the comforts of our home, I think it's only fair that you help keep it clean and comfortable. And I am so grateful when you do your jobs. Did you know that?"
If you keep the conversation relaxed and non-judgemental, and report your own feelings and needs honestly, she may well get it that her participation is an important part of your family dynamics, and that YOU DO APPRECIATE her help.
We often, as busy parents, forget the "thank you" part, though that may not be a problem with you since she still craves your approval. But maybe you could be extra-careful to notice even her smaller moments of cooperation. You may have to train yourself to watch for those. And don't make a huge deal out of it – just a smile and thank you or quick hug may be just the acknowledgement she needs.
There's a very helpful book called How to Talk So Kids Will Listen, and Listen So Kids Will Talk. You can learn how your children can propose their own solutions to all sorts of classic family problems.
Read a sample of this wonderful parent-workshop-between-covers here: http://www.amazon.com/How-Talk-Kids-Will-Listen/dp/038081.... I think you'll be impressed with the possibilities.