  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 $R\approx 2\,\mu\text{m}$, 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.
