Are there any chemical methods for getting rid of weeds in organic growing?

There are no approved herbicides in organic growing. There are materials that are approved, but methods must also be approved as well. I will give you an example. It is possible to spray horticultural oil with sulfur (and add some soap to really make sure) and "fry" some weeds and everything else. All these items are approved in organic growing, but this use is not. The only methods that are approved are mechanical: Pulling or cultivation by hand or with the use of implements or smothering them with mulch. There are some folksy formulas out there that they say will work. They don't. Weeds recover much more quickly than what you want to grow. That is their nature. What works best is a hoe and some judiciously applied mulch.

There is a "pre-emergent" spray made from corn silk that inhibits weed seed germination. Apply it when you set seedlings out, then lay down a layer of mulch.

Intercropping, or interplanting is also a strategy organic gardeners use to inhibit weeds. Seedlings of short-season vegetables like spinach, lettuce, and Asian greens are planted on tight spacing to fill in the gaps between main-season crops like tomatoes, peppers, broccoli, and eggplants. They grow up and create a "living mulch" that overshadows weeds. Weed seeds that do germinate come up in the shade of these plants, so they're spindly and small. After a few weeks, the intercropped plants are harvested, and the main crop plants take over the bed.