The chiral β-nitroacrylate 2 derived from the (R)- or (S)-4-(3-hydroxy-4,4-dimethyl-2-oxopyrrolidin-1-yl) benzoic acid 1 acts as a reactive dienophile in a diastereoselective Diels-Alder reaction with 1,3-cyclohexadiene. The major cycloadducts have been isolated and transformed into enantiopure trans(2S,3S)- or (2R,3R)-N-Boc-3-aminobicyclic[2,2,2]octane-2-carboxylic acids 5. The trans-(2S,3S)- or (2R,3R)-N-Boc 3-(hydoxymethyl)-2-aminobicyclic[2,2,2]octane 6 derivatives were also obtained.