We propose Thomson scattering of short pulse laser beams by low energy electron beams at a right angle for generation of femtosecond d X-rays. The basic idea is the observation that a low emittance electron beam can be focussed much more tightly in a transverse dimension than in the longitudinal dimension. Therefore much shorter pulses of X-rays can be generated (in the direction of the electron beam) by arranging the laser beam to meet the electron beam at a right angle rather than head on as in the Thomson backscattering configuration. Simple analysis of the process is presented by noting the similarity between the Thomson scattered radiation and the well-understood undulator radiation. Using the parameters of the recently developed femtosecond visible lasers and the high brightness electron guns, it is shown that 1 angstrom X-ray pulses, of 300 fs duration, containing several 10(5) photons within 10% bandwidth per collision, can be generated.