Question
I live in Illinois near Chicago. My soil is not
good, mostly clay, almost everything I plant dies.
I also am not really good at maintaiing plants.
My question: is there a low maintenance perennial
that will grow in mostly clay soil?

Answer
Eileen,
Unfortunately not many.
I know how you fell because I endured lots of back breaking digging and tilling just to get it broke up.Then you should get out all the biggest clumps.After that add some good compost or organic material.If you don't have a compost pile yet,I recommend getting one or even making your own.
When I lived in the country I just dug about a 3 ft wide and 4 feet deep hole in my back yard hidden behind the garage. Throw in grass clippings,raw vegetable scraps like carrot peels,lettuce,cabbage,banana peels,fall leafs and to really enrich your pile,get some aged cow manure(you can tell it is aged if it doesn't offensive odor or big bags of ready made compost or an organic mix with fertilizer already added.Perlite is also good to mix in.It looks like tiny styrofoam balls and they let your compost aquire oxygen for fast decomposition.Peat moss is also a great amendment to clay soil.Throw all these in together and turn the pile every few days with a spade or pitch fork.OR...

If it is in your budget you should consider getting a round barrel type of compost that turns with a handle. The turning of the the material speeds up decomposition.They usually have vents to catch rain as well,which it needs as well.You may find them at larger garden centers like Lowes or Home depot.If not you can make a homemade one or order one online.
iF YOU KEEP IT FULL AND TURN IT REGULARLY AND KEEP ADDING STUFF,YOU COULD HAVE COMPOST IN AS soon as a years time.
Of course there are plants that tolerate dry hard soil(not many,but some).Even low maintenance plants have to have a good start in the right soil to develop a strong root system.That's what makes them low maintenance.It's all in the soil.Period. Here are a few places to look for composters and some plant sites to find dry soil plants.
Charlies Greenhouse & Gardens,Gardens Alive,Park Seed,Wayside Gardens,Gardeners Supply,Walters Perennials,White Flower Farm,Bluestone Perennials,Forest FarmThompson & Morgan..Also lots of herbs like dry soil.
Hope this helps.I know your frustration.