The Fe1+yTe1−xSex compounds belong to the family of iron-based high temperature superconductors, in which superconductivity often appears upon doping antiferromagnetic parent compounds. Unlike other Fe-based superconductors (in which the antiferromagnetic order is at the Fermi surface nesting wavevector [ 1 /2, 1 /2,1]), Fe1+yTe orders at a different wavevector, [ 1 /2, 0, 1 /2]. Furthermore, the ordering wavevector depends on y, the occupation of interstitial sites with excess iron; the origin of this behavior is controversial. Using inelastic neutron scattering on Fe1.08Te, we find incommensurate magnetic fluctuations above the Néel temperature, even though the ordered state is bicollinear and commensurate with gapped spin waves. This behavior can be understood in terms of a competition between commensurate and incommensurate order, which we explain as a lock-in transition caused by the magnetic anisotropy. Superconductivity in the recently-discovered ironbased superconductors (FeSCs) 1 often appears at high transition temperatures. These compounds contain a simple square lattice of iron atoms, coordinated with pnictogen or chalcogen atoms forming planes of tetrahedra. Interplanar layers differ between families, consisting of either metal oxides, alkaline earth atoms, alkali atoms, or nothing at all as in the "11" compounds on which we focus here. The parent compounds of most families become orthorhombic and antiferromagnetic (AFM) at low temperatures, and superconductivity can be induced by doping with electrons, holes, isoelectronically, or by the application of pressure (see, e.g., 2 ). Their high-T c superconductivity may be related to the magnetic order 3 , which seems to be the result of Fermi surface nesting 4 . There is also intrinsic interest in magnetism in these materials, but it has not been as extensively explored.While nesting explains many experiments, the magnetic order in the x = 0 endpoint of the Fe 1+y Te 1−x Se x series is a highly unusual commensurate "bicollinear" magnetic structure 5 with a wavevector along q AF M = [ 1 /2 , 0, 1 /2]. Neither density functional theory (DFT) 6 nor photoemission measurements 7 find any evidence for nesting at this wavevector, which indicates the presence of local moments. These moments must interact with each other via competing exchange interactions 8 , which should lead to incommensurate order. The mechanism behind the commensurate bicollinear order is one of the main unresolved issues in the effort to understand the FeSCs.Here we report results of a detailed inelastic neutron scattering (INS) investigation of the region near q AF M in a high-quality single-crystal sample of Fe 1.08 Te. We find strong evidence for competition between commensurate and incommensurate ordering in the form of spin excitations which abruptly shift from the incommensurate q inc ≈ [0.45, 0, 0.5] to the commensurate wavevector q AF M = [ 1 /2 , 0, 1 /2] when passing below the Néel temperature T N (see Fig. 1). We interpret this unusual behavior in terms of a lock-in transition d...