To shrink electrical circuits beyond the looming practical limits of Moore's Law, it has been a common goal to create carbon-based components. Here is the first example of a new class of donor-sigma-acceptor rectifiers: hemibiquinones (HBQs). HBQs possess donor and acceptor moieties that are electronically isolated by inter-ring torsion. A HBQ-dinitrile self-assembles on a template-stripped gold surface through directed chemisorption, forming a 1.1nm-thick monolayer. Rectification is measured through the monolayer or single molecules by using three different top electrode arrangements. Even though the HBQs are composed of relatively weak electrophores, rectification ratios ranging from 5 to 160 were observed at 2.5V.