Preheat the grill w/all burners on high for 10 minutes (lid down).
Wash the squash, pat down dry. Trim the tops and bottoms, then rub olive oil over them.
Once the gill is hot, turn off the center burner, turn the other burners to medium. Put the whole squash over the center burner, close the lid and cook until easily pierced with the tip of a sharp knife/fork. Depending on the size of the squash, this will take approximately 12-20 minutes.
Turn the squash as needed.
Transfer the squash to a cutting board, slice, then toss with the parsley, salt and pepper.