We demonstrate excitation of a single trapped cold 40 Ca + ion to Rydberg levels by laser radiation in the vacuum-ultraviolet at 122 nm wavelength. Observed resonances are identified as 3d 2 D 3/2 to 51 F, 52 F and 3d 2 D 5/2 to 64 F. We model the lineshape and our results imply a large state-dependent coupling to the trapping potential. Rydberg ions are of great interest for future applications in quantum computing and simulation, in which large dipolar interactions are combined with the superb experimental control offered by Paul traps.PACS numbers: 37.10. Ty, 32.80.Ee, 42.50.Ex The properties of Rydberg atoms are dominated by one electron being in a state of high principal quantum number, which causes long lifetimes and large dipole moments [1,2]. This results in giant dipolar interactions between Rydberg atoms [3] which enable the formation of ultralong-range molecules [4], quantum logic gate operations between two neutral atoms [5,6], and the control of the state of transmitted light through a Rydberg sample at the single photon level [7]. A completely new approach to this field of research is the Rydberg excitation of trapped ions [8,9,10], which aims to combine the long-range Rydberg-blockade mechanism, demonstrated in the case of neutral atoms confined in optical lattices [11,12,13], with the superb level of control over single ions achieved in Paul traps [14,15]. Rydberg ions in Coulomb crystals will allow for shaping localized vibrational modes for quantum simulation and fast parallel execution of quantum gates [16,17]. Further applications are dynamical structural phase transitions and non-equilibrium dynamics driven by Rydberg excitations [18].Two major challenges have to be met in order to access the unique features of Rydberg ions: Firstly, excitation energies are large compared to the case of neutral atoms such that either a vacuum ultraviolet (VUV) laser source [9,19] or multi-step excitation [20] with UV lasers is required. Secondly, the large polarizability of Rydberg states makes them very susceptible to residual electric fields in the Paul trap, where an oscillating field with quadrupolar geometry and gradients of about 10 7 -10 9 V/m 2 provides stable trapping conditions. Ions are confined near the node (field-zero) of the electric quadrupole, nevertheless residual fields at the position of the ion perturb the Rydberg state and lead to a shifted and broadened resonance.In this Letter we present laser excitation of a single trapped cold ion to Rydberg states. Ions are initialized in the metastable 3d 2 D 3/2 or 3d 2 D 5/2 state before they are excited to the 51 F and 52 F (from D 3/2 ) respectivly 64 F (from D 5/2 ) state using vacuum ultraviolet radiation near 122 nm. By applying a state dependent fluorescence measurement following the decay of the Rydberg state, population transfer out of the initial D-state is detected. The polarizability of the Rydberg ion is deduced from the observed line-shift and -broadening, caused by residual electric fields in the trap.Experiments were carried o...