A compact laser synchrotron source (LSS) is proposed as a means of generating tunable, narrow bandwidth, ultra-short pulses of hard x rays. The LSS is based on the Thomson backscattering of intense laser radiation from a counterstreaming electron beam. Advances in both compact ultra-intense solid-state lasers and high brightness electron accelerators make the LSS an attractive compact source of high brightness pulsed x rays, particularly at photon energies beyond approximately 30 keV. The x-ray wavelength is lambda[angstrom] = 650 lambda0[mum]/E(b)2[MeV], where lambda0 is the laser wavelength and E(b) is the electron beam energy. For E(b) = 72 MeV and lambda0 = 1 mum, x rays at lambda = 0.12 angstrom (100 keV) are generated. The spectral flux, brightness, bandwidth, and pulse structure are analyzed. In the absence of filtering, the spectral bandwidth in the LSS is typically less than or similar to 1% and is limited by electron beam emittance and energy spread. Two configuration of the LSS are discussed, one providing high peak power and the other moderate average power x rays. Using present day technology, the LSS can generate picosecond pulses of x rays consisting of > 10(9) photons/pulse with a peak brightness of greater than or similar to 10(20) photons/s mm2 mrad2 (0.1% BW) and photon energies ranging from 50 to 1200 keV.