Pull or smother.

Your other thread, same topic & with several response: http://forums.gardenweb.com/discussions/2965069/natural-solutions-for-this-patch-possibly-chickweed?n=2

Chickweed prefers growing in good garden soils, near neutral soil pH, lots of available Nitrogen, and it is a prolific seeder and roots from stem pieces easily.

The picture posted earlier does not show any Chickweed, other not easily identified plants but no Chickweed.

http://extension.psu.edu/pests/weeds/weed-id/common-chickweed

kimmq is kimmsr