Generally speaking, the existence of a superluminal neutrino can be attributed either to re-entrant Lorentz violation at ultralow energy from intrinsic Lorentz violation at ultrahigh energy or to spontaneous breaking of fundamental Lorentz invariance (possibly by the formation of a fermionic condensate). Re-entrant Lorentz violation in the neutrino sector has been discussed elsewhere. Here, the focus is on mechanisms of spontaneous symmetry breaking. It is possible that OPERA's claimed discovery [1] of a superluminal muon-type neutrino does not come from the violation of Lorentz invariance but from unknown factors in the clock-synchronization process [2] or from a purely statistical effect [3]. In fact, it has been shown [4] that OPERA's claimed value (v νµ −c)/c ∼ 10 −5 is ruled out by the expected but unobserved energy losses from electron-positron-pair emission (ν µ → ν µ + e − + e + ), at least, as long as there exists a preferred frame from the Lorentz violation. Still, the claim by OPERA has provided new impetus for the discussion on the possible sources of Lorentz violation. In order to engage in this discussion, let us assume that OPERA's result is correct qualitatively (existence of a superluminal muon-neutrino) even if not quantitatively (most likely, |v νµ − c|/c ≪ 10 −5 ). Condensed-matter physics, which possesses an analog of Lorentz invariance (LI), now suggests several different scenarios of Lorentz violation (LV). Among them are: (1a) LI is not a fundamental symmetry but an approximate symmetry which emerges at low energies and is violated at ultrahigh energies (cf. [5]). (1b) Intrinsic LV at ultrahigh energies gives an emergent Lorentz-invariant theory at lower energies but ultimately, at or below an ultralow energy scale, induces a re-entrant violation of LI (see, e.g., Sec. 12.4 of [6]).(2) LI is fundamental but broken spontaneously (see, e.g., [7,8] and references therein).In this Letter, we discuss the spontaneous breaking of Lorentz invariance (SBLI), that is, the spontaneous appearance of a preferred frame in the vacuum, which can be derived from Lorentz-invariant physical laws. The order parameter of SBLI can be a vector field b α (for example, the vector field of Fermi-point splitting [9,10] or an aether-type velocity field [11]), an emergent tetrad-type field e α a [12,13,14,15], or any other field which is covariant but not invariant under Lorentz transformations.If SBLI occurs only in the neutrino sector, which interacts weakly with the charged-matter sector, then SBLI has no direct impact on this other matter (certain indirect quantum-loop effects can be suppressed by near-zero mixing angles). The non-neutrino matter essentially does not feel the existence of the preferred reference frame. In fact, it is very well possible that SBLI occurs only for the neutrino field, because the other fermions have already experienced electroweak symme-1