We show that the dipole-dipole interaction between three identical Rydberg atoms can give rise to bound trimer states. The microscopic origin of these states is fundamentally different from Efimov physics. Two stable trimer configurations exist where the atoms form the vertices of an equilateral triangle in a plane perpendicular to a static electric field. The triangle edge length typically exceeds R ≈ 2 µm, and each configuration is two-fold degenerate due to Kramers' degeneracy. The depth of the potential wells and the triangle edge length can be controlled by external parameters. We establish the Borromean nature of the trimer states, analyze the quantum dynamics in the potential wells and describe methods for their production and detection. PACS numbers: 34.20Cf,32.80.Ee,82.20.Rp Rydberg atoms [1] are ideal candidates for the investigation of few-body quantum phenomena for several reasons. First, their internal and external degrees of freedom can be accurately controlled and manipulated in stateof-the-art experiments. This gives rise to theoretically well-understood and tunable dipole-dipole (DD) interactions [2, 3] between ultra-cold Rydberg atoms. Second, the range of these DD interactions is extremely large -it typically extends to several microns. This feature allows the study of few-body quantum systems whose constituents can be prepared, manipulated and detected individually. Several quantum phenomena arising from strong interactions between two Rydberg atoms were investigated recently. Examples are given by the Rydberg blockade effect [4][5][6][7] and the realization of quantum gates and entanglement [8,9]. Rydberg atoms can form giant diatomic molecules via different binding mechanisms between their constituents [10][11][12][13][14][15]. Artificial gauge fields induced by the DD interaction [16,17] and acting on the relative motion of two Rydberg atoms were predicted in [18][19][20].In few body-physics, systems with three particles often show qualitatively different features as compared to two particles [21][22][23][24][25][26][27][28][29][30][31]. For example, it has been shown [21] that the dipole blockade can be broken by adding a third Rydberg atom. Furthermore, it has been predicted [22] that systems of more than two DD interacting atoms exhibit conical intersections [23,24], which are relevant for photo-chemical processes. A paradigm of few-body quantum physics is the Efimov effect [25][26][27][28]. Here a short-range resonant two-body interaction between identical bosons gives rise to a universal set of bound trimer states [29]. Recently, it was shown that the Efimov effect persists [30] even for a resonant long-range DD interaction.Here we show that the DD interaction between three distant Rydberg atoms with non-overlapping electron clouds can induce bound trimer states. These states arise from the rich internal level structure of the Rydberg atoms. A crucial point is the presence of several dipole transitions in each atom and the interplay between distance-dependent DD interactions and ...