We demonstrate the realization of a quantum register using a string of single neutral atoms which are trapped in an optical dipole trap. The atoms are selectively and coherently manipulated in a magnetic field gradient using microwave radiation. Our addressing scheme operates with a high spatial resolution and qubit rotations on individual atoms are performed with 99 % contrast. In a final read-out operation we analyze each individual atomic state. Finally, we have measured the coherence time and identified the predominant dephasing mechanism for our register.PACS numbers: 32.80.Pj, 39.25.+k, 42.50.Vk Information coded into the quantum states of physical systems (qubits) can be processed according to the laws of quantum mechanics. It has been shown that the quantum concepts of state superposition and entanglement can lead to a dramatic speed up in solving certain classes of computational problems [1,2]. Over the past decade various quantum computing schemes have been proposed. In a sequential network of quantum logic gates quantum information is processed using discrete one-and two-qubit operations [3]. Another approach is the oneway quantum computer which processes information by performing one-qubit rotations and measurements on an entangled cluster state [4]. All of these schemes rely on the availability of a quantum register, i. e. a well known number of qubits that can be individually addressed and coherently manipulated. There are several physical systems, such as trapped ions [5,6,7], nuclear spins in molecules [8], or magnetic flux qubits [9] that can serve as quantum registers.Neutral atoms exhibit favourable properties for storing and processing quantum information. Their hyperfine ground states are readily prepared in pure quantum states including state superpositions and can be well isolated from their environment. In addition, using laser cooling techniques, countable numbers of neutral atoms can be cooled, captured and transported [10,11]. The coherence properties of laser trapped atoms have been found to be adequate for storing quantum information [12,13]. Moreover, controlled cold collisions [14] or the exchange of microwave [15] or optical [16,17] photons in a resonator offer interesting schemes for mediating coherent atom-atom interaction, essential for the realization of quantum logic operations.In our experiment we use a string of an exactly known number of neutral caesium atoms. The atoms are trapped in the potential wells of a spatially modulated, light induced potential created by a far detuned standing wave dipole trap [10,18]. They can be optically resolved with an imaging system using an intensified CCD camera (ICCD) [19,20]. Our experimental setup is schematically depicted in Fig. 1. Two focussed counter-propagating Nd:YAG laser beams at a wavelength of λ = 1064 nm FIG. 1: Scheme of the experimental setup. Two focussed counter-propagating Nd:YAG laser beams form the dipole trap. We illuminate the trapped atoms by an optical molasses and split the fluorescence light with a beamsplit...