Phys.Rev.Lett.99:042501,2007 Properties of finite nuclei are evaluated with two-nucleon (NN) and three-nucleon (NNN) interactions derived within chiral effective field theory (EFT). The nuclear Hamiltonian is fixed by properties of the A=2 system, except for two low-energy constants (LECs) that parameterize the short range NNN interaction. We constrain those two LECs by a fit to the A=3 system binding energy and investigate sensitivity of 4He, 6Li, 10,11B and 12,13C properties to the variation of the constrained LECs. We identify a preferred choice that gives globally the best description. We demonstrate that the NNN interaction terms significantly improve the binding energies and spectra of mid-p-shell nuclei not just with the preferred choice of the LECs but even within a wide range of the constrained LECs. At the same time, we find that a very high quality description of these nuclei requires further improvements to the chiral Hamiltonian.