I kept waiting for the little pink blossoms of Allium schoenoprasum.
I guess I didn't read the seed packet very well.
Garlic chives, Allium tuberosum, also called Chinese chives.
These chives have flat leaves and sweetly fragrant white flowers which bloom in August. Garlic chives are used just as regular chives are: a culinary herb, an ornamental and in cut flower arrangements. Cutting for bouquets will assure that they don't seed all over the garden.