  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.
