Definitely not burning it, but pyrolysis has been suggested (basically "burn" it in an oxygen-free environment).
The plastics are heated to about 500 °C in the absence of oxygen. The longer molecules break into liquid fractions like naphtha and diesel, solid cuts like waxes, and lower-molecular-weight gases. In most plants, roughly 10% of the product is char, a by-product.
It's not without its drawbacks. Some gases are produced, and those are either burned to (partially?) power the pyrolysis process or are flared off. About 10% is reduced to char and would have to be disposed of conventionally (unsure of the environmental impact of that).
I don't have time right now to dive deep into the topic (just throwing off what I do know plus a link that explains it), but it's possible it's less harmful overall than just throwing it in a landfill forever. (Assuming the input energy for the reaction chamber comes from clean sources.)