The configuration interaction method is used to demonstrate that there is an electronically stable state of positronic calcium with an orbital angular momentum of L 1. This prediction relies on the use of an asymptotic series to estimate the variational limit of the energy. The best estimate of the binding energy is 37 meV. A discussion of the structure of the system is also presented. DOI: 10.1103/PhysRevLett.97.183402 PACS numbers: 36.10.Dr In 1997 the existence of positron-atom bound states was demonstrated by two independent calculations [1,2] of the e Li ground state. Subsequently, it has been shown that at least nine other atoms can attach a positron and form an electronically stable bound state [3]. Besides its intrinsic interest, the knowledge that positrons can form bound states has been crucial to recent developments in understanding the very large annihilation rates that occur when positrons annihilate with various molecules in the gas phase [4 -7]. The problem of explaining the large annihilation rates had remained essentially unresolved almost since the first experiments [8][9][10]. While the possible influence of bound states upon the annihilation rate had been conjectured [11,12], the lack of hard evidence for the existence of positron-atom bound states had certainly inhibited development of compound state models of positron-molecule annihilation [12 -15]. The prevailing view on positron binding [16] has changed to such an extent over the last decade that a positron-atom (or positron-molecule) interaction potential that supports a positron bound state can now be regarded as mundane [17].One feature of the atomic calculations is that binding has only been seen for spherically symmetric states. The angular momentum of the parent atom ground state and the positron-atom composite state are always zero [3]. Another feature is that binding occurs to atoms with an ionization energy close to 6.80 eV (the Ps binding energy) and the binding energies are largest for atoms with their ionization energies closest to 6.80 eV [3].While the existence of positron binding to atoms (and molecules) is now accepted, the question of whether these complexes have excited states is largely unexplored. Whether such states exist is best determined by calculations that are sufficiently sophisticated to accurately model the delicate interplay of attractive and repulsive Coulomb interactions with the additional complication of an angular momentum barrier. (We note the prediction of a 2 P o state of e Mg by Gribakin et al. [18]. However, the many body theory of Gribakin et al. is known to grossly overestimate the strength of the positron-atom interaction [3,[19][20][21] and so the result has never been taken seriously). First, it is necessary to identify what is meant by an excited state. The states of interest should have the same long-range dissociation channel as the lower-lying positronic atom ground state. This is to distinguish these systems from states which are better described as a positron bound to an excited state...