Using polarization-resolved resonant Raman spectroscopy, we explore collective spin excitations of the chiral surface states in a three dimensional topological insulator, Bi2Se3. We observe a sharp peak at 150 meV in the pseudovector A2 symmetry channel of the Raman spectra. By comparing the data with calculations, we identify this peak as the transverse collective spin mode of surface Dirac fermions. This mode, unlike a Dirac plasmon or a surface plasmon in the charge sector of excitations, is analogous to a spin wave in a partially polarized Fermi liquid, with spin-orbit coupling playing the role of an effective magnetic field.Magnets and partially spin-polarized Fermi liquids support collective spin excitations (spin waves), in which all electron spins respond coherently to external fields, and the "glue" that locks the phases of precessing spins is provided by the exchange interaction. In nonmagnetic materials where inversion symmetry is broken but time-reversal invariance remains intact, strong spin-orbit coupling (SOC) may play the role of an effective magnetic field, which locks electron spins and momenta into textures. This phenomenon is encountered in threedimensional (3D) topological insulators (TIs), which harbor topologically protected surface states [1][2][3][4][5]. These states have been a focus of intense studies, both from the fundamental point-of-view [6][7][8][9][10][11][12] and for potential applications in spintronics devices [13][14][15][16][17][18][19][20]. However, the many-body interactions leading to collective effects in TIs remain largely unexplored. An essential aspect of this physics is an interplay between the Coulomb interaction and SOC, which is expected to give rise to a new type of collective spin excitations -chiral spin waves [21][22][23][24][25][26]. In the long wavelength (q = 0) limit, these modes are completely decoupled from the charge channel and thus distinct from spin-plasmons [27,28], Dirac plasmons [29,30], and surface plasmons in TIs [30,31].In this Letter, we employ polarization-resolved resonant Raman spectroscopy, a technique of choice for probing the collective charge [32,33], spin [34][35][36][37] and orbital excitations [38], to study collective spin excitations of the chiral surface states in Bi 2 Se 3 . To enhance the signal from the surface states, we tune the energy of incoming photons in resonance with a transition between two sets of chiral surface states: near the Fermi energy and about 1.8 eV above it [ Fig. 1(a)] [39]. We observe a long-lived excitation at 150 meV in the pseudovector symmetry channel of the Raman spectra, which is most pronounced at low temperatures but persists up to room temperature. By comparing the data with calculations, we identify this excitation as the transverse collective chiral spin mode supported by spin-polarized surface Dirac fermions. Such collective modes -first predicted for nontopological systems [21][22][23][24][25][26]36] but hitherto unobserved -are "peeled off" from the continuum of particle-hole excitations by t...