If using raw beets, wash them clean of sand and dirt. Set aside to air dry or dry well with a towel or paper towel. If using roasted beets, proceed to food processor step.
Toss the beets in a mixing bowl with oil, thyme, a few pinches of salt and about 15 grinds of pepper.
Turn the beets out onto a baking sheet and roast until fork tender, shaking the pan occasionally to insure even cooking, about 40 minutes.
Remove beets from oven and set aside to cool. (You can do this up to a couple days ahead of time if you store them sealed in the refrigerator.)
Remove and discard the skins from the beets. Cut beets into quarters. Add the beet quarters to a food processor or blender. Pulse a few times until beets are roughed up into small but still chunky pieces.
Dump the blended beets into a serving bowl. Crumble the goat cheese into the beets and add the chives and lemon juice. Toss together and season with salt and pepper, to taste.