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We present precise phase-connected pulse timing solutions for 16 γ-ray-selected pulsars recently discovered using the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope plus one very faint radio pulsar (PSR J1124− 5916) that is more effectively timed with the LAT. We describe the analysis techniques including a maximum likelihood method for determining pulse times of arrival from unbinned photon data. A major result of this work is improved position determinations, which are crucial for multiwavelength follow-up. For most of the pulsars, we overlay the timing localizations on X-ray images from Swift and describe the status of X-ray counterpart associations. We report glitches measured in PSRs J0007+ 7303, J1124− 5916, and J1813− 1246. We analyze a new 20 ks Chandra ACIS observation of PSR J0633+ 0632 that reveals an arcminute-scale X-ray nebula extending to the south of the …