I expect the previous owner put down the woodchips, because the area under a big old tree is a very difficult area to grow grass. The tree not only shades it out, but sucks up most of the moisture and nutrients.
It would be easier to grow a shade garden under your tree than grass. Here's some suggestions of plants:
solomon seal, heuchera, bleeding heart, pulmonaria, wild ginger, tiarella, lily of the valley, sweet woodruff, lamium, epimedium, liriope. All of them are shade plants and mostly pretty tolerant of dry shade, but you will likely have to provide some water to help them get established.
If you don't mind providing water on an on-going basis (not just while they are getting established), you could plant ferns, hostas, astilbes.
Here's a couple other threads where we have had discussions of planting under trees: