Star Tickseed [Coreopsis pubescens] found at Fletcher Park on 5 June 2013. It’s a member of the Aster (Asteraceae) family. Wild Flowers of North Carolina, which names it just Coreopsis, page 201, states that it starts blooming in July, but this is obviously an earlier sighting, and it “grows on dry slopes and in open woods in our mountain and piedmont counties.”
USDA Plants Listing: https://plants.usda.gov/home/plantProfile?symbol=COPU2