Depending on where you want to grow your ground cover and what you want to cover, my thoughts bring me to Creeping Thyme/ Common Garden Thyme it grows about 4/6 inch high at the most, can be cut by mower, clings close to ground, spreads out 6-9 inches, it has the usual purple flowers and the smell when trampled on is wonderful, can be used in cooking too. if it is tramples on it just stands back up again but don't play football on it as that's a step too far.
There is also a yellow leaf plant the same name, it smells of lemons and a mixture of both is fab. grow from seed around March time, in trays and thin out when large enough to hold, grow on till the plants are big enough to be planted outside, IF you live in cold frost areas in winter, you can cover these young plants with the white horticultural fleece to give a bit protection, but next year they should be able to live outdoors like other shrubs if you can grow them.
Others to try:
Ajuga, (can get out of hand by spreading tiny new plants)
Vinca (spreads when it touches ground at the tips of long tentacles)
There are many more that would suit but IF you can tell what you want to cover and the area like pathway, border etc, then maybe others can come in with even better suggestions.
Good Luck. WeeNel.
The cheapest ground cover, grown from seed, is a lawn. You can add things like clover (Dutch White Clover, around here- I do not know if it grows in Chicago) or other flowers that stay low. English Daisy will grow in a lawn (well, it does in Golden Gate Park!). You can direct seed certain grass species that do not need to be mowed. Make a natural meadow.
The next place to look is the area of erosion control. Even if you are not seeding a hillside, the seeds that are sold in larger volumes are a good price, and a good way to get started. Local suppliers will be the best to consult about what species and varieties will do what you want. Around here (Central coast area of CA) there are many vetches and clovers that are used for direct seeding, and several species of grass. All the other plants are thought of as wildflower seed and are added in small amounts for show. The grasses are deep rooted for best erosion control, and the legumes provide the grasses with nitrogen.
Here are some questions to ask yourself before you talk to a seed company:
1) Will you irrigate in dry seasons?
2) How long do you want it to last? Is this temporary cover until you can plant something else later this year? Does it have to last 2-3 years? Is it permanent?
3) How much sun does the area get?
4) How steep is the area?
5) How tall do you want it to grow?
6) Can you access the area with equipment like a rototiller or tractor? How well can you prepare the soil?
To find local suppliers of large volumes of seed I would google "Seed Wholesale Illinois" and "Hydroseed Chicago Illinois" and see if any of the companies that come up can help you.
Of course, you can answer those questions here in this thread and get a lot more specific answers.