Unconventional superconductivity typically emerges in the presence of quasi-degenerate ground states, and the associated intense fluctuations are likely responsible for generating the superconducting state. Here we use polarized neutron scattering to study the spin space anisotropy of spin excitations in Fe1.07Te exhibiting bicollinear antiferromagnetic (AF) order, the parent compound of FeTe1−xSex superconductors. We confirm that the low energy spin excitations are transverse spin waves, consistent with a local-moment origin of the bicollinear AF order. While the ordered moments lie in the ab-plane in Fe1.07Te, it takes less energy for them to fluctuate out-of-plane, similar to BaFe2As2 and NaFeAs. At energies above E 20 meV, we find magnetic scattering to be dominated by an isotropic continuum that persists up to at least 50 meV. Although the isotropic spin excitations cannot be ascribed to spin waves from a long-range ordered local moment antiferromagnet, the continuum can result from the bicollinear magnetic order ground state of Fe1.07Te being quasi-degenerate with plaquette magnetic order. PACS numbers: 74.25.Ha, 78.70.Nx Unconventional superconductivity in cuprate and heavy fermion superconductors emerge in the vicinity of multiple exotic orders that are quasi-degenerate in energy [1][2][3][4], providing a plethora of fluctuations that may enhance or even generate superconductivity. Iron-based superconductors are found close to several different magnetic instabilities [5][6][7][8][9][10][11][12][13][14], suggesting an important role for magnetism in their superconductivity [15,16]. In addition, these materials may exhibit quasi-degenerate ground states, realized through magnetic frustration and electron correlations [17,18]. These interactions are epitomized in the iron chalcogenide FeTe 1−x Se x series, with magnetism evolving from bicollinear (BC) magnetic order in Fe 1+y Te [7,19] towards competing stripe and Néel fluctuations without static magnetic order in FeSe [20]. Understanding the nature of magnetic fluctuations and manifestations of magnetic frustration is therefore a key step towards elucidating the physics of these materials.Compared to the parent compounds of iron pnictides that order at the in-plane wave vector Q = (0.5, 0.5) of the paramagnetic tetragonal unit cell corresponding to the nesting wave vector of electron and hole Fermi surfaces (stripe AF order) [21,22], the parent compound of iron chalcogenide superconductors Fe 1+y Te orders at or near Q = (0.5, 0) [7,19], despite sharing a similar electronic structure with the iron pnictides [23,24]. Furthermore, Fe 1+y Te exhibits significantly larger ordered moments [7,19] and stronger electronic correlations [25] than iron pnictides. These results point to localized magnetism in Fe 1+y Te, although the presence itinerant carriers can cause damping of the magnetic excitations.At low interstitial iron concentrations (y < 0.12), Fe 1+y Te exhibits long-range BC order with the ordering vector Q = (0.5, 0) and ordered moments along the b-ax...