Carbon monoxide (CO) is one of the primary coolants of gas and an easily accessible tracer of molecular gas in spiral galaxies but it is unclear if CO plays a similar role in metal poor dwarfs. We carried out a deep observation with IRAM 30 m to search for CO emission by targeting the brightest far-IR peak in a nearby extremely metal poor galaxy, Sextans A, with 7% Solar metallicity. A weak CO J=1-0 emission is seen, which is already faint enough to place a strong constraint on the conversion factor (a_CO) from the CO luminosity to the molecular gas mass that is derived from the spatially resolved dust mass map. The a_CO is at least seven hundred times the Milky Way value. This indicates that CO emission is exceedingly weak in extremely metal poor galaxies, challenging its role as a coolant in these galaxies.