Catalyzes the ATP-dependent condensation of cysteine and glutamate to form the dipeptide gamma-glutamylcysteine (gamma-GC), the first and rate-limiting step in the production of glutathione (GSH). ATP + L-cysteine + L-glutamate = ADP + gamma-L-glutamyl-L-cysteine + H(+) + phosphate Feedback inhibition by glutathione. Sulfur metabolism; glutathione biosynthesis; glutathione from L-cysteine and L-glutamate: step 1/2. Present with 5130 molecules/cell in log phase SD medium. Belongs to the glutamate--cysteine ligase type 3 family.