Chicago Meat Sharing
I'm not certain what you mean by a meat share program. But you can buy fresh, farm raised meat from C&D Family Farms. They offer a CSA program and sell their products at different market locations city-wide. I don't know where you are located...Tuesdays from 4 to 7PM the truck is located on Ashland at Berwyn (Andersonville). I regularly purchase their fresh eggs - delicious. I have also tried ground turkey, ground beef, pork shoulder, pork chops and have enjoyed all.
Perhaps their CSA program is similar to what you are looking for...???