The highly structured magnetic field and plasma properties observed in the heliospheric extension of the coronal streamer belt have been interpreted as evidence for multiple current sheets originating at coronal helmet streamers. We explore the linear stability of a simple case: a triple current sheet, as would exist above two neighboring helmets of the same polarity. The behavior of the triple current sheet when perturbed by small disturbances can be described (in the incompressible limit) by MHD Orr-Sommerfeld and Squire equations, which we solve with a Chebyshev-&tgr; method. We show the velocity and magnetic fields which characterize the three unstable modes and describe the modal dependence on fieldwise wavenumber and current sheet separation. At long wavelengths an unexpected phenomenon occurs: two modes degenerate into unstable traveling modes. We also explore the three-dimensional behavior and the modal variation with both large and small values of the resistivity and viscosity. We conclude that the magnetic topology in closely packed streamers is susceptible to instabilities with growth times of the order of hours. Our predictions indicate that the resultant plasmoid structures should be observable with the large angle and spectrometric coronagraph (LASCO) and ultraviolet coronagraph spectrometer (UVCS) instruments on the upcoming Solar and Heliospheric Observatory (SOHO) mission. ¿ American Geophysical Union 1995