We have developed microwave kinetic inductance detectors suitable for near-IR single-photon counting. Our films are made of titanium and titanium nitride, deposited in a multilayer structure Ti/TiN/Ti/TiN with a total thickness of 44 nm. The film has a transition temperature of 1.2 K and a surface kinetic inductance of 34 pH/sq. The resonator was designed with lumped elements and consists of two blocks of interdigitated capacitors connected by a meandered stripe inductor. The resonator resonance frequency is 6.8 GHz, and the internal quality factor is 125,000. The detector is read out with the usual homodyne scheme and calibrated with light pulses produced by a laser diode with wavelength 1550 nm. For the 0- and 1-photon peaks, we measure a FWHM energy resolution of 0.44 eV and 0.56 eV, respectively. This resolution is sufficient to resolve events with up to 4 photons.