Could it be thistle? If you don't want to use chemicals the best solution is to dig it out. Try to get as much of the roots as possible as they will sprout new weeds. If they are dug when quite small it isn't hard to get the roots.

Welcome to the battle, my friend. As, mnwsgal says, it sounds like Canadian thistle. They are difficult to eradicate as they spread by underground runners and seed. I pull quite a few everyday. They're sneaky buggers too, usually hiding under the leaves at the base of my garden plants. Be ever vigilant.

Here is a link that might be useful: Canada thistle info.

Could also be a plant related to both called wild lettuce - same solution!

I planted chicory once and now, many years later, still get volunteers. Could be what you've got is sprouting from roots, could be a "seed bank" as it's called. Mulching helps, as does putting in enough other plants - and close enough - to provide competition for sun and water.

I prefer to call them creeping thistle - they are not native and does not come from Canada. Chicory is still rare enough in Minnesota - I hardly seen any, mostly in the Lake Minnetonka Area while Creeping Thistle is much too common. Bull Thistle usually is in very low numbers less than 5 per 1/4 acre yard is not unusual thought as stubborn as usual, when their flower stalks doesn't form, they remains a perennial not a biennial.