Bindweed

My daughter and her husband bought an older home and the yard is filled with BINDWEED! How does one rid the yard of this noxious plant? Please help! We grow vegetables as well and do not want to use chemicals to kill this plant.
I look forward to your response.
Thanks,
Donna
Donna, your email box was full so I'm posting my answer here.
This is a tough one. The empathetic gardener thinks, “The plant needs energy which it gets from the sun. The only way it can get this energy is through leaves. If I can keep it from having leaves, it will eventually die.”
I have only dealt with it in gardens which is curious since I have extensive mowed areas. Bindweed must have been or still be in some of these areas since, I suppose, it was already present when I converted sod to garden. In my reference books (including Weeds of Lawn and Garden) I only find solutions for dealing with it in cultivated soil. The books say to till or cultivated repeatedly, every other week or sooner and that this may take more than one growing season. When my son was preteen I would pay him and a friend by the ounce for the "gold" roots. Perhaps I didn't pay enough or use the right motivation because, though he and his friend loved to dig, they tired of gold mining too soon. When my Tom Sawyer plan failed I found myself out there digging up the rhizomes. It was just a matter of keeping after them, getting as many as I could in the time I had and keeping an eye on the patch and going after any as they appeared above ground.
For the lawn I would probably just mow and see what happens. If it doesn't get worse, I'd forget about it and accept bindweed as part of the diversity of my organic lawn. I have a ground ivy that shares a lot of my lawn and has spread over the years but it doesn't bother me. However, if you want to get rid of bindweed without tilling up the whole lawn and keeping it that way for most of a year, I suggest going after it one stem at a time on hands and knees with a hand lawn weeding tool. This tool is about 18 inches long including the handle and has a V shaped end that you stick in the ground at an angle to cut the stem below ground surface. They will keep coming and you will have to keep after them. Pick a small patch to work on and keep after it until the bindweed is gone then move on to another patch. This will be a test of your persistence.