I don't know what you mean by- no till. You couldn't till under a tree anyway. If you are looking for some kind of plant that would do well under a tree try lamium. It has white and green leaves and clusters of purple flowers in late June. It is fast growing and takes plenty of abuse. I have it edging my flower bed that goes up to a tree and I am forever pulling off parts because it is crowding out my Hosta. You would only need 3 or 4 plants and it would fill in. You would have to dig out clumps occasionally

Oh, I have plenty of lovelies to put under the tree - hosta, astilbe, pulmonaria, brunnera, anemone, ajuga, ferns, and yes - georgeous lamium. But I'll keep my eye on it ;)

I was hoping to just smother the existing grass and weeds with newspaper, cutting through to plant, and then topping with wood chips. I want to avoid using any chemical weedkillers, but I also don't want to create bigger problems in the future.

Do you think it can work?

I did something similar in a couple of different ways: 1. put (wet) cardboard/newspaper in a fairly thick layer. Cover with rotted manure & compost. Let this sit for a couple of weeks. when you dig, the cardboard/newspaper should be mostly rotted & the weeds killed.
2. Turn sod/soil. Cover with several inches of compost/manure. Cover all that with heavy plastic (I got mine from a local farm that cuts it off their silage pile), use rocks to weight down edges. cut holes larger than the plants, in order to allow for growth & water to get to the soil & to avoid rotting the roots. Plant & cover it all with mulch. You can't see the plastic, but it keeps weeds down, holds moisture in & helps warm/insulate the ground in the spring here in my Zone 3.

I too have used the smother method. It worked well. If you have a weed trimmer a very close shave first gets you off on the right direction. Hosta are great for these spots. I have put one eye in a hole I could barely eak out of between roots and they have managed to find their way in and around the roots and filled in nicely.

Good to hear. I don't plan on tilling, since it is a maple with very shallow roots, but I do like the idea of topping with compost, and that the hostas will fill out nicely.

Thank you.