We report near-infrared and submillimeter line and continuum measurements toward the embedded source IRAS 23011+6126 in the Cepheus E molecular cloud. The source has a luminosity of 70 +/- 10 L⊙ and is not detected in the 2 μm continuum. Its spectral energy distribution is characterized by a very low bolometric temperature (Tbol = 60 K), placing it in the class 0 category. The source is associated with a relatively compact (0.18 pc) molecular cloud core with a mass of 8 M⊙. Also associated with this source are four lobes of outflowing molecular gas. These lobes can easily be grouped into two well-collimated bipolar outflow structures with position angles differing by 52°. The small-scale outflow structure is associated with strong line emission from vibrationally excited molecular hydrogen with line ratios consistent with C shocks, while the large-scale outflow structure shows no associated molecular hydrogen emission. If one source is responsible for both flows, then the outflow mechanism must be both temporally and angularly variable. An alternate possibility is that the observed luminosity and outflow structures are generated by two sources, separated by less than 104 AU on the sky. Both of these sources must be very deeply embedded, and presumably quite young.