Ways to fix a chipped tooth?

Here's the deal: I chipped my front tooth and the dentist suggested veneers, but the thought of them having to shave off my teeth scares me. Should I just ask for them to file my teeth down? What about Lumineers? The chip is not huge, but I think it's noticeable and it makes me feel self conscious. I don't want to loose too much tooth structure, and quite frankly I don't have much money to shell out, but I do want a solution that will last. Any suggestions relevant to the matter would be greatly appreciated and rewarded :)