To prepare the squash, use a potato peeler to remove the skin. Cut off and discard the ends, then carefully cut the squash into ½ inch slices. For the slices that have seeds, use a spoon to remove and discard the seeds and guts of the squash. Brush olive oil on both sides of the squash.
Heat a BBQ or grill pan over medium-high heat. You could alternatively use a frying pan if you don't have either, you just won't get the pretty grill marks). Grill the butternut squash slices, covered, for about 4 - 5 minutes per side until grill marks are formed and the slices are fork tender. You may need to do this in batches.
Serve the butternut squash hot, spooning over the chimichurri sauce to taste. You could also sub the chimichurri for other sauces you enjoy or even just some salt and pepper on the butternut squash for a simple side dish.