We have mapped the submillimeter continuum emission from the rich star-forming core, rho Oph A, at 3.50, 450, 800, and 1300 mum using the JCMT and IRAM 30 m telescopes. In addition to the diffuse emission from the cloud core itself, these observations reveal four well-defined clumps, which, surprisingly, are barely visible in the single-dish molecular maps obtained so far in this region. The gas may have partially frozen out onto the dust grains, due to low temperature and/or high density in the clumps. We discuss the possibility that these clumps are prestellar or extremely young, low-mass protostars. One of them coincides with the (centimeter) radio source VLA 1623 which drives one of the youngest and best collimated CO bipolar flows known to date. Supplementing our JCMT measurements with stringent upper limits obtained at all four IRAS bands by maximum entropy deconvolution of the raw IRAS data, we show that VLA 1623 is a highly obscured (A(V) greater than or similar to 1000) young stellar object (YSO) with a remarkably low bolometric luminosity (L(bol) less than or similar to 1 L.) and dust temperature (T(d) less than or similar to 20 K). Its spectral energy distribution is well fitted by a single modified blackbody from dust at 15-20 K with an opacity index beta = 1.5. This indicates a mass of circumstellar material M(C) approximately 0.6 M. and a bolometric luminosity L(bol) approximately 1 L.. Our submillimeter observations resolve a nearly spherical dust envelope around VLA 1623, of FWHM size almost-equal-to 2000 AU roughly independent of wavelength. This suggests that the bulk of the circumstellar mass of VLA 1623 is distributed in an '' apple-like '' structure rather than a disk. Detailed, spherical modeling of this dust structure, using the radiative transfer code of Wolfire & Cassinelli, shows the spectral energy distribution and submillimeter intensity profiles of VLA 1623 can be fitted simultaneously by a 1 L. internal source surrounded by a circumstellar envelope with a surprisingly shallow density distribution [rho(r) is-proportional-to r-0.5]. The remarkably cold temperature, high internal obscuration, and relatively massive circumstellar structure of VLA 1623 all point to an extremely young object, perhaps a true protostar. We compare VLA 1623 with a few other very young embedded sources similarly characterized by very low values of the ratio L(bol)/L(submm), and suggest that these objects define an entirely new class of YSOs, which we call ''Class 0'' to indicate their extreme youth. Although these strong submillimeter YSOs are invisible in the near- and mid-IR, they are already powering highly collimated outflows (opening angles < 30-degrees) with great efficiency (L(flow)/L(bol) up to approximately 50%). This may indicate that the outflow phenomenon starts earlier than previously thought in (proto)stellar evolution, i.e., prior to the near-IR Class I phase as in the scheme devised by Lada.
