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 manipulating 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 $sim4$), 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.