  CoRoT, the pioneer space-based transit search, steadily provides thousands of
high-precision light curves with continuous time sampling over periods of up to
5 months. The transits of a planet perturbed by an additional object are not
strictly periodic. By studying the transit timing variations (TTVs), additional
objects can be detected in the system.
  A transit timing analysis of CoRoT-1b is carried out to constrain the
existence of additional planets in the system.
  We used data obtained by an improved version of the CoRoT data pipeline
(version 2.0). Individual transits were fitted to determine the mid-transit
times, and we analyzed the derived $O-C$ diagram. N-body integrations were used
to place limits on secondary planets.
  No periodic timing variations with a period shorter than the observational
window (55 days) are found. The presence of an Earth-mass Trojan is not likely.
A planet of mass greater than $\sim 1$ Earth mass can be ruled out by the
present data if the object is in a 2:1 (exterior) mean motion resonance with
CoRoT-1b. Considering initially circular orbits: (i) super-Earths (less than 10
Earth-masses) are excluded for periods less than about 3.5 days, (ii)
Saturn-like planets can be ruled out for periods less than about 5 days, (iii)
Jupiter-like planets should have a minimum orbital period of about 6.5 days.
