We present high angular resolution observations of the Class 0 protostar IRAM 04191+1522 , using the Submillimeter Array ( SMA ) . The SMA 1.3 mm continuum images reveal within IRAM 04191+1522 two distinct sources with an angular separation of 7.8 \pm 0.2 ^ { \prime \prime } . The two continuum sources are located in the southeast-northwest direction , with total gas masses of \sim 0.011 M _ { \odot } and \sim 0.005 M _ { \odot } , respectively . The southeastern source , associated with an infrared source seen in the Spitzer images , is the well-known Class 0 protostar with a bolometric luminosity of \sim 0.08 L _ { \odot } . The newly-discovered northwestern continuum source is not visible in the Spitzer images at wavelengths from 3.6 to 70 \mu m , and has an extremely low bolometric luminosity ( < 0.03 L _ { \odot } ) . Complementary IRAM N _ { 2 } H ^ { + } ( 1–0 ) data that probe the dense gas in the common envelope suggest that the two sources were formed through the rotational fragmentation of an elongated dense core . Furthermore , comparisons between IRAM 04191+1522 and other protostars suggest that most cores with binary systems formed therein have ratios of rotational energy to gravitational energy \beta _ { rot } > 1 % . This is consistent with theoretical simulations and indicates that the level of rotational energy in a dense core plays an important role in the fragmentation process .