We present the first ab initio calculations for p-shell single-Λ hypernuclei. For the solution of the manybaryon problem, we develop two variants of the no-core shell model with explicit Λ and Σ + , Σ 0 , Σ − hyperons including Λ-Σ conversion, optionally supplemented by a similarity renormalization group transformation to accelerate model-space convergence. In addition to state-of-the-art chiral two-and three-nucleon interactions, we use leading-order chiral hyperon-nucleon interactions and a recent meson-exchange hyperon-nucleon interaction. We validate the approach for s-shell hypernuclei and apply it to p-shell hypernuclei, in particular to 7 Λ Li, 9 Λ Be and 13 Λ C. We show that the chiral hyperon-nucleon interactions provide ground-state and excitation energies that generally agree with experiment within the cutoff dependence. At the same time we demonstrate that hypernuclear spectroscopy provides tight constraints on the hyperon-nucleon interactions. PACS numbers: 21.80.+a, 21.60.De, 13.75.Ev, 05.10.Cc Over the past decades, the structure of hypernuclei has been the focus of a number of experimental programs worldwide, providing a wealth of high-precision data on excitation spectra as well as binding energies [1][2][3][4][5][6]. These experimental efforts continue and are intensified, e.g., in several present and future experiments at international facilities like J-PARC, JLab, and FAIR. Hypernuclear structure theory has a rich history of phenomenological models that have accompanied and driven the experiments, most notably, the shell model for p-and sdshell hypernuclei [7,8], cluster models [9-12], various meanfield models [13][14][15][16], or recent Monte Carlo calculations with simplified phenomenological interactions [17,18]. Ab initio calculations based on realistic nucleonic and hyperonic interactions were limited to systems of up to 4 nucleons so far [19][20][21][22]. Nevertheless, these calculations established a direct link between experimental observables and the underlying interactions and helped to elucidate the role of hyperons in matter. Advancing ab initio methods beyond their current limits is highly desirable. It would allow to exploit the wealth of accurate experimental data, e.g., on p-shell hypernuclei, for constraining and improving the underlying interactions and to make predictions for yet unobserved phenomena.There are two main aspects that hindered ab initio calculations for p-shell hypernuclei in the past. Firstly, a prerequisite are accurate ab initio calculations of the non-strange parent nucleus. The approach has to be able to provide converged results for the parent nucleus and the nucleonic Hamiltonian has to yield a good description of the experimental nuclear spectra. In the past few years, ab initio methods using two-nucleon (NN) and three-nucleon (3N) interactions constructed in chiral effective field theory (EFT) succeeded to provide a quantitative description of ground states and spectra of nuclei in the p-shell and beyond [23,24]. This is facilitated by a multitude ...