Abstract We report on results from GBT/ARGUS ¹²CO(1-0) observations for the giant low surface brightness galaxy Malin 1, which allow us to determine an upper limit for its CO mass, and hence its molecular gas mass and molecular gas mass surface density Σ H 2 . Although we performed very deep observations through 17 hr on-source integration time, reaching a noise level of ∼0.2 mK (T A * ) with a corresponding extended source CO limit (3σ) of 0.09 K km s⁻¹, 19 times more sensitive than previous works, we do not detect the ¹²CO(1-0) emission line. However, the observations allow us to estimate an upper limit (3σ) for the CO mass of about 7.4 × 10⁹ M _⊙ for the extended emission, and 1.4 × 10⁸ M _⊙ for the central part of the galaxy. With these figures we conclude that the molecular gas surface density is lower than 0.3 M _⊙ pc⁻², and the corresponding molecular to atomic gas mass ratio is lower than 0.13. The evidence suggests quite different physical conditions for the interstellar medium in Malin 1 compared to that of normal, high surface brightness spirals. This, in one way to another, keeps an usual molecular gas tracer as CO hidden from our observations, in spite of the diverse stellar and structural properties of Malin 1 observed by several authors since more than 30 yr.