This looks like Bishops Weed (Aegopodium podagraria)
 which is an aggressive invasive, spreading plant. 
Also known as 'Goutweed,' it is often first purchased in an attractive variegated form with green and white leaves but eventually reverts back to straight green.
 It is a creeping perennial that can grow to three feet and gets flat-topped white flowers (in sun areas) that look similar to Queen Ann's Lace.
It grows from long roots called rhizomes, which not only allow it to spread, but makes it difficult to weed out as any pieces left behind can sprout.
You can try smothering with a tarp to prevent photosynthesis. This method depletes the carbohydrate reserve, thus weakening the plant. You'd want to start this soon so the plant is unable to grow and store reserve energy in the roots. It may not be completely successful or need to be used over a long period of time.
Otherwise chemical control is an option, with the careful application of a pesticide containing the active ingredient
 glyphosate, which is a non-selective systemic herbicide which translocates throughout the plant into the roots/rhizomes for a complete kill. Even this may need to be done more than once for this tenacious plant.
Read all label instructions carefully and do not allow the product to get on desirable plants nearby.

Christine

Thanks Christine!  I pulled it up last fall and laid cardboard and mulch over the area. And used glyphosate on the new sprouts. It sure is difficult to get rid of. 

Just monitor for a possible additional application to keep at it.

Good luck!

Emily