We report on Chandra observations of the TeV emitting High Mass X-ray Binary LS 5039, for a total exposure of ~70ks, using the ACIS-S camera in Continuos Clocking mode to search for a possible X-ray pulsar in this system. We did not find any periodic or quasi-periodic signal in the 0.3-0.4 and 0.75-0.9 orbital phases, and in a frequency range of 0.005-175 Hz. We derived an average pulsed fraction 3sigma upper limit for the presence of a periodic signal of ~15% (depending on the frequency and the energy band), the deepest limit ever reached for this object. If the X-ray emission of LS 5039 is due (at least in part) to a rotational powered pulsar, the latter is either spinning faster than ~5.6 ms, or having a beam pointing away from our line of sight, or contributing to ~15% of the total X-ray emission of the system in the orbital phases we observed.
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