The University of California Extension lists the use of benefin, pendimethalin, oryzalin and dicamba for the control of chickweed. The are sold under different tradenames.
Products containing benefin, pendimethalin and oryzalin are pre-emergence herbicides that control weeds by retarding the germination of weed seeds. Dicamba is a postemergence herbicide that controls actively growing chickweeds. These herbicides are safe for use on grass, as cited by the University of California Extension.
Recommended herbicides are often incorporated in the weed and feed lawn fertilizers and effectively control chickweeds as lawns are fertilized. Avoid using dicamba near broadleaf ornamental plants or food crops. Use benefin and pendimethalin in established grass and avoid using on vegetables. You can use oryzalin near the nonbearing nut and fruit trees.