Centaurs are small Solar system objects orbiting between Jupiter and Neptune. They are widely believed to be escapees from the trans-Neptunian region on their way to become Jupiter-family comets. Indeed, some Centaurs exhibit the characteristic cometary appearance. The sublimation of carbon monoxide has been proposed as a driver of activity in distant comets, but no strong detection of gaseous CO in a Centaur other than 29P/Schwassmann-Wachmann 1 has been reported to date. Here we report the results of a deep search for CO outgassing in three Centaurs: (315898), (342842), and (382004). Our survey was carried out using the Caltech Submillimeter Observatory on nine nights in late 2011. The targeted rotational line J(2-1) of CO is undetected in all three objects in spite of high instrumental sensitivity. We find the model-dependent 3 sigma upper limits to the CO production rate of 2.13 x 10(27) molecules s(-1) for (315898), 1.32 x 10(27) molecules s(-1) for (342842), and 1.17 x 10(27) molecules s(-1) for (382004), which are among the most sensitive obtained to date. These upper limits are consistently analysed in the context of published CO data of 14 Centaurs and one well-observed long-period comet, C/1995 O1 (Hale-Bopp), and support an earlier suggestion that the surfaces of most Centaurs are not dominated by exposed CO ice.