  We present high angular resolution observations of the Class 0 protostar
IRAM04191+1522, using the Submillimeter Array (SMA). The SMA 1.3 mm continuum
images reveal within IRAM04191+1522 two distinct sources with an angular
separation of 7.8\,$\pm$\,0.2$"$. The two continuum sources are located in the
southeast-northwest direction, with total gas masses of about 0.011 M_sun and
about 0.005 M_sun, 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 about 0.08 L_sun. The newly-discovered
northwestern continuum source is not visible in the Spitzer images at
wavelengths from 3.6 to 70 micron, and has an extremely low bolometric
luminosity (< 0.03 L_sun). Complementary IRAM N2H+(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 IRAM04191+1522 and other protostars suggest that most cores
with binary systems formed therein have ratios of rotational energy to
gravitational energy $\beta_{\rm rot}$ > 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.
