We report the operation of quantum wire (QWR) semiconductor diode lasers fabricated by cleaved edge overgrowth. The active region in these index guided lasers consists of 15 QWRs formed at the right angle intersection of 15 [001] oriented quantum wells (QWs) each 7 nm wide, with a single 7-nm-wide QW grown along the [110] direction. Doping with Be and Si in the two orthogonal growth directions leads to the formation of a linear p-n junction in which the QWRs are embedded. Efficient current injection into the wires is demonstrated by the almost complete suppression of optical emission from QW states as well as by threshold currents as low as 0.4 mA for uncoated devices at 4.2 K.