We present recent observations of quiet regions near the center of the solar disk using the Advanced Stokes Polarimeter. These observations reveal a component of the solar magnetic field heretofore unobserved: isolated, small-scale (typically 1"-2" or smaller), predominantly horizontal magnetic flux structures in the solar photosphere. These features occur in isolation of the well-known, nearly vertical flux concentrations usually seen in the photospheric "network." Hence we ascribe this horizontal flux to the photospheric "internetwork." They reveal themselves by the distinct signature of the Stokes Q and U polarization profiles, which are symmetric about the line center. The polarization signals are weak, with peak amplitudes typically ˜0.1%-0.2% of the continuum intensity in the resolved spectral profiles, but they are well above the noise level of these observations (≍0.05%). Such magnetic fields are weak (significantly less than 1000 G) and largely horizontal owing to the absence, or near absence, of accompanying Stokes V polarization when observed at the center of the solar disk. These horizontal field elements are often associated with blueshifted Stokes line profiles, and they often occur between regions of opposite polarity (but weak) Stokes V profiles. The horizontal elements are short-lived, typically lasting ˜5 minutes. Our observations suggest that we are viewing the emergence of small, concentrated loops of flux, carried upward either by granular convection or magnetic buoyancy. Even though these entities show weak field strengths, they also seem to be fairly common, implying that they could carry the order of 1024 Mx of magnetic flux to the surface on a daily basis. However, further observational study is needed to identify the specific nature of this phenomenon.