I don't know what it is. It doesn't look like a weed though. It looks more like a flower. If you really want to get rid of it spray it with round up. Round up works through the foliage and neutralizes when it hits the soil. Be careful to protect what you don't want killed because the spray will kill anything it lands on. A piece of cardboard acts as a good barrier. Spray when you are going to have a couple of sunny days. It works slowly. In a couple of days you will notice wilting and in a couple of weeks it will be brown and dead and you can start digging

It looks like goutweed to me...aka ground elder aka aegopodium. My sympathies to you in your upcoming time of sorrow.....I also have it.....Waaaaah!!!!

newine, thank you! The internet tells me it'll grow back from any little piece, so it looks like we've got our work cut out for us. I really don't like the idea of using round up though, so I think I'll take the risk.

Looks like goutweed to me too. I quite like it - under strictly controlled conditions only. If you do decide to dig - the roots and rhizomes are quite shallow, so you'll be able to thin it out a lot.
Connie

I also have goutweed but it doesn't look like that - mine's variegated green & white and the leaves aren't waxy-looking, they're more papery and they haven't come up yet in my area (Northern Ontario).
It's true it's invasive but I agree with prairierose that under controlled conditions it's manageable. My patch is growing in a bed hemmed in on all sides by the lawn so it doesn't spread (so far).

There is quite a difference between the variegated and the plain green....somewhat like the difference between Yogi Bear and King Kong. I also have the variegated and I actually managed to kill it by accident....for me the variegated is a non invasive ground cover.The solid green though......underneath the surface of the soil is a vaste network of roots...growing, spreading, invading...well you get the idea.

I had some of the solid green appear on me - probably from seed, I'm thinking. It was quite amazing. I thought I'd plant both kinds in a little space between a retaining wall and gravel. The solid green grew twice as fast, with leaves twice as big - it was almost scary. By the way, charbucks, I have fairly light soil and I've found the easiest way to dig up the roots is with a garden fork - I can rip up roots and rhizomes and leave most of the soil behind. I did this in a fairly large section of a flower bed two years ago, and had just a bit grow back on me, mostly tight in around other plants where I couldn't really get everything out.
Connie

I wonder what would happen if you planted bamboo, goutweed and lily of the valley in the same spot.

I do have one bed under a tree that has goutweed, creeping bellflower, and goldenrod in it. Maybe I should add some lily of the valley? So far, the goutweed and goldenrod seem to be doing better than the bellflower, but maybe it will come from behind. Would that be good or bad? I actually planted it that way on purpose - all the bad boys in one place.
Connie