Whereas spintronics brings the spin degree of freedom to electronic devices, molecular/organic electronics adds the opportunity to play with the chemical versatility. Here we show how, as a contender to commonly used inorganic materials, organic/molecular based spintronics devices can exhibit very large magnetoresistance and lead to tailored spin polarizations. We report on giant tunnel magnetoresistance of up to 300% in a (La,Sr)MnO3/Alq3/Co nanometer size magnetic tunnel junction. Moreover, we propose a spin dependent transport model giving a new understanding of spin injection into organic materials/molecules. Our findings bring a new insight on how one could tune spin injection by molecular engineering and paves the way to chemical tailoring of the properties of spintronics devices. ; Comment: Original version. Revised version to appear in Nature Physics.