The effect of anomalous chromomagnetic (mu) and chromoelectric couplings (d) of the gluon to the top quark are considered in e+ e- --> t tbar, with unpolarized and longitudinally polarized electron beams. The total cross section, as well as t and tbar polarizations are calculated to order alpha_s in the presence of the anomalous couplings. One of the two linear combinations of t and tbar polarizations is CP even, while the other is CP odd. The limits that could be obtained at a typical future linear collider with an integrated luminosity of 50 1/fb and a total c.m. energy of 500 GeV on the most sensitive CP-even combination of anomalous couplings are estimated as -3 < Re(mu) < 2 for Im(mu) = 0 = d, and sqrt{Im(mu)^2 + |d|^2} < 2.25 for Re(mu) = 0. There is an improvement by roughly a factor of 2 at 1000 GeV. On the other hand, from the CP-odd combination, we derive the possible complementary bounds as -3.6 < Im(mu^* d) < 3.6 for Im(d) = 0, and -10 < Im(d) < 10 for Im(mu^* d) = 0, at a c.m. energy of 500 GeV. The corresponding limit for 1000 GeV is almost an order of magnitude better for Im(mu^* d), though somewhat worse for Im(d). Results for the c.m. energies 500 GeV and 1000 GeV, if combined, would yield independen limits on the two CP-violating parameters of -0.8 < Im(mu^* d) < 0.8 and -11 < Im(d) < 11.
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