Stable colloidal solutions of Ag2S quantum dots with a size of 2–3 to 28–30 nm were synthesized by a hydrochemical deposition in low-concentration water solutions of silver nitrate, sodium sulfide, and sodium citrate. A large absolute value of the measured zeta potential of colloidal solutions, a small change in the size of quantum dots and zeta potential during long-term storage of solutions for 1000 days after synthesis indicate their high temporal stability. The synthesized colloidal solutions were dispersed in a solution of polyvinyl alcohol. The resulting films of Ag2S quantum dots in a PVA matrix are flexible and have a thickness of no more than 0.03 mm. The use of the PVA matrix to prepare films with Ag2S quantum dots promotes the preservation and increase in the stability of colloidal particles due to their fixation in the polymer matrix. For the first time, the optical properties of Ag2S quantum dots of different sizes in PVA films were determined. Decreasing the size of Ag2S quantum dots to 2.6 nm leads to an increase in the band gap of silver sulfide to 1.85 eV. It is shown that repeated bending of the films has practically no effect on the Eg value of Ag2S quantum dots.