  In this paper, we consider the set of interfaces between + and - spins
arising for the critical planar Ising model on a domain with + boundary
conditions, and show that it converges towards CLE(3).
  Our proof relies on the study of the coupling between the Ising model and its
random cluster (FK) representation, and of the interactions between FK and
Ising interfaces. The main idea is to construct an exploration process starting
from the boundary of the domain, to discover the Ising loops and to establish
its convergence to a conformally invariant limit. The challenge is that Ising
loops do not touch the boundary; we use the fact that FK loops touch the
boundary (and hence can be explored from the boundary) and that Ising loops in
turn touch FK loops, to construct a recursive exploration process that visits
all the macroscopic loops.
  A key ingredient in the proof is the convergence of Ising free arcs to the
Free Arc Ensemble (FAE), established in [BDH16]. Qualitative estimates about
the Ising interfaces then allow one to identify the scaling limit of Ising
loops as a conformally invariant collection of simple, disjoint SLE(3)-like
loops and thus by the Markovian characterization of [ShWe12] as a CLE(3).
  A technical point of independent interest contained in this paper is an
investigation of double points of interfaces in the scaling limit of critical
FK-Ising. It relies on the technology of [KeSm12].
