Short answer: Chelation does not work to unclog arteries.
There were enough advertised claims, without evidence, that the FDA wrote a warning in 2010. (via the Wikipedia article on Chelation therapy)
The U.S. Food and Drug Administration today warned eight companies that their over-the-counter (OTC) chelation products are unapproved drugs and devices and that it is a violation of federal law to make unproven claims about these products. There are no FDA-approved OTC chelation products.
The companies that received the warning letters claim that their products treat a range of diseases by removing toxic metals from the body. Some also claim to treat autism spectrum disorder, cardiovascular diseases, Parkinson’s disease, Alzheimer’s disease, macular degeneration, and other serious conditions. Some companies that received the warning letters also claim their products will detect the presence of heavy metals to justify the need for chelation therapy.
The drug products involved have not been evaluated by the FDA for treatment of these diseases, and violate the Federal Food, Drug, and Cosmetic Act (FFDCA). Despite the claims of the companies that received warning letters, the effectiveness in treating any of the diseases listed is unsubstantiated.
The University of Maryland Medical Center summarises the evidence for EDTA treatment:
So far, there is no good evidence that EDTA chelation therapy is effective for heart disease. Proponents believe it may help people with atherosclerosis (hardening of the arteries) or peripheral vascular disease (decreased blood flow to the legs) by clearing clogged arteries and improving blood flow. However, the few studies that show it may help have been poorly designed, making the results questionable.
The theory that EDTA clears clogged arteries and improves blood flow is based on an outdated model about what causes heart disease. Other newer theories include the possibility that EDTA functions like an antioxidant, preventing damaging molecules known as free radicals from injuring blood vessel walls and allowing plaque to build up. These ideas are just theories, however.
Most good clinical studies examining EDTA chelation therapy for heart disease and vascular disorders have found that it is no better than placebo. For example, one scientifically rigorous study comparing EDTA chelation therapy to placebo in 84 people with heart disease concluded that those receiving EDTA chelation did no better than those receiving placebo in terms of changes in exercise capacity and quality of life. Several studies evaluating EDTA chelation therapy for peripheral vascular disease did not find any difference between those receiving EDTA and those receiving placebo.
References are provided on that page.
Quackwatch gives a detailed overview of the history of this pseudoscience, some of the proposed mechanisms and their rebuttals, and more information on how the hypothesis was tested and rejected, and the work done by authorities to stop the propagation of the claim.