M.,
A little over a year ago, a mother made a very similar post about her 5 year old, so, I dragged up my response to yet again, expose myself as a reformed thief. :)
I cannot believe that I'm putting this in writing for people to see, but when I was 8, I was a little klepto. Occasionally, when in a nearly-caught situation, I lied my way out of it. I didn't turn into a career criminal or habitual liar. The lies were simply self preservation. But, after getting caught a few times, getting the "whoopin" and having to face the person from whom I'd stolen, to apologize and return the item, I stopped doing it. Just be consistent, and don't let some thefts go unpunished.
I would further add to that post that there were some reasons behind my thievery that I see now. I didn't steal things just to do it. They were always things that I wanted and for one reason or another didn't need or "deserve." Now, I'm not saying go out and get her everything she wants so that she doesn't steal one, but instead, when she's busted, discuss with her why she wanted that, what she already has that is a suitable alternative and why it is so important not to take things from others. You might explain why this is wrong (in your own words and beliefs) and how sad it makes the victim. They had that item because they wanted it, and that it is unfair that she took it away.
When we see things that we wish we had, we can make it a goal to obtain it by saving allowance, getting it as a reward or as a gift on the next special occasion. That way, it is ours and we can be proud of it and not be afraid that someone will see and recognize it as their own missing item.
With consistency and very close observation, this can be "nipped in the bud."
Best wishes,
B.