Farmer Vicki of Genesis Growers is making her first spring delivery tomorrow. She uses hoop houses.
I've been picking up spring greens (pea shoots, lettuce) for the last month or so at Farmers' Markets in Oak Park and environs.
Spring-like produce is definitely available. Have you tried the Green Grocer?
http://www.greengrocerchicago.com/
"Don't you ever underestimate the power of a female." Bootsy Collins