Light-matter interaction at the atomic scale rules fundamental phenomena such as photoemission and lasing while enabling basic everyday technologies, including photovoltaics and optical communications. In this context, plasmons, the collective electron oscillations in conducting materials, are important because they allow the manipulation of optical fields at the nanoscale. The advent of graphene and other two-dimensional crystals has pushed plasmons down to genuinely atomic dimensions, displaying appealing properties such as a large electrical tunability. However, plasmons in these materials are either too broad or lying at low frequencies, well below the technologically relevant near-infrared regime. Here, we demonstrate sharp near-infrared plasmons in lithographically patterned wafer-scale atomically thin silver crystalline films. Our measured optical spectra reveal narrow plasmons (quality factor of ∼4), further supported by a low sheet resistance comparable to bulk metal in few-atomic-layer silver films down to seven Ag(111) monolayers. Good crystal quality and plasmon narrowness are obtained despite the addition of a thin passivating dielectric, which renders our samples resilient to ambient conditions. The observation of spectrally sharp and strongly confined plasmons in atomically thin silver holds great potential for electro-optical modulation and optical sensing applications.