Conversion of two diametrically opposed atomic rows on a carbon nanotube to sp(3) hybridization produces two identical weakly coupled one-dimensional electronic systems within a single robust covalently bonded package: a biribbon. Arm-chair tubes, when so divided, acquire a pair of narrow spin-polarized bands at the Fermi energy; interaction across the sp(3) dividers produces a tunable band splitting in the THz range. For semiconducting tubes, the eigenvalues of the low-energy electronic states are surprisingly unaffected by the bifurcation; however, the tubes' response functions to external electric fields are dramatically altered. These modified tubes could be produced by uniaxial compression transverse to the tube axis followed by site-selective chemisorption.