We present a 5 \arcmin \times 5 \arcmin integrated intensity map of ^ { 12 } CO ( J = 3 - 2 ) emission from the \rho Ophiuchi cloud core that traces low-luminosity outflow emission from two protostars : Elias 29 and , most likely , LFAM 26 . The morphology of the outflow from Elias 29 is bipolar and has a curved axis that traces the S-shaped symmetry seen in H _ { 2 } emission . The outflow from LFAM 26 is a new detection and oriented in the east/west direction near the plane of the sky with most of the blue-shifted emission being absorbed by intervening clouds . The outflow axis of this object also appears to intersect a knot of H _ { 2 } emission previously attributed to Elias 29 . LFAM 26 is a low luminosity source ( L _ { bol } = 0.06 \ > L _ { \sun } ) which , in combination with the observed outflow , makes it a candidate Very Low Luminosity Object ( VeLLO ) . We derive lower limits to the gas column densities and energetics for both outflows . The mechanical luminosities for Elias 29 and LFAM 26 are 6.4 and 10.3 \times 10 ^ { -3 } \ > L _ { \sun } , respectively .