I love chickweed. Picking it seems to encourage more to grow (by shaking the seeds out over a wider area, I suppose). It's an excellent plant to have around.
Incidentally, you can use it in salads and soups yourself.
Just watch out, there's a weed that looks very similar and isn't edible. It often grows right next to chickweed. The way to tell the difference is to examine the stem closely. Chickweed has a thin single line of hairs growing vertically up each stem, while the weed stem is hairy all round. Also if you break the stem in half, chickweed contains a long thin string (not there in the similar weed).
cheers
Erica