We report on a 95ks Chandra observation of the TeV emitting High Mass X-ray Binary LSI +61 303, using the ACIS-S camera in Continuos Clocking mode to search for a possible X-ray pulsar in this system. The observation was performed while the compact object was passing from phase 0.94 to 0.98 in its orbit around the Be companion star (hence close to the apastron passage). We did not find any periodic or quasi-periodic signal (at this orbital phase) in a frequency range of 0.005-175 Hz. We derived an average pulsed fraction 3 sigma upper limit for the presence of a periodic signal of ~10% (although this limit is strongly dependent on the frequency and the energy band), the deepest limit ever reached for this object. Furthermore, the source appears highly variable in flux and spectrum even in this very small orbital phase range, in particular we detect two flares, lasting thousands of seconds, with a very hard X-ray spectrum with respect to the average source spectral distribution. The X-ray pulsed fraction limits we derived are lower than the pulsed fraction of any isolated rotational-powered pulsar, in particular having a TeV counterpart. In this scenario most of the X-ray emission of LSI +61 303 should necessarily come from the interwind or inner-pulsar wind zone shock rather than from the magnetosphere of the putative pulsar. Furthermore, we did not find evidence for the previously suggested extended X-ray emission (abridged).
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