Well, I think the most obvious candidates for avant garde food are Alinea, Avenues, Moto, Tru, Charlie Trotter's, and Schwa. As discussed above, I would agree with others that they also produce food that tastes exceedingly good; in fact, I don't think they sacrifice taste at all. If they did, they probably wouldn't be considered among the very best restaurants in the city (along with Everest and Spiaggia, neither of which is all that avant garde compared with the previous group, but are still excellent and among Chicago's best).
I really don't consider Blackbird avant garde at all; it's simply delicious food, in a contemporary vein. (Maybe that's a better word for what you're seeking, rather than the leading edge that often involves molecular gastronomy?) If you enjoy the food at Blackbird and are looking for something similar - sinfully outstanding food, in the same contemporary genre - then I would start with one sixtyblue, and then quickly add North Pond, Aigre Doux, Sweets and Savories, Custom House, and Spring. If you would consider restaurants in the suburbs, then also consider Vie (Western Springs), Michael (Winnetka), Tallgrass (Lockport), Oceanique (Evanston), and Chef's Station (Evanston). If you enjoy contemporary Italian, then consider Cafe Spiaggia, Coco Pazzo, Vivere, Trattoria No. 10, and Pane Caldo in the city, and in the suburbs, Va Pensiero (Evanston), Gabriel's (Highwood), and Bacino's Trattoria (LaGrange).