  We present a new vacuum solution of Einstein's equations describing the near
horizon region of two neutral, extreme (zero-temperature), co-rotating,
non-identical Kerr black holes. The metric is stationary, asymptotically near
horizon extremal Kerr (NHEK), and contains a localized massless strut along the
symmetry axis between the black holes. In the deep infrared, it flows to two
separate throats which we call "pierced-NHEK" geometries: each throat is NHEK
pierced by a conical singularity. We find that in spite of the presence of the
strut for the pierced-NHEK geometries the isometry group SL(2,R)xU(1) is
restored. We find the physical parameters and entropy.
