Scanning force microscopes routinely operate with forces in the piconewton range, but new applications such as cantilever-based magnetometry and magnetic resonance force microscopy demand force resolutions that can be a million times smaller. The minimum detectable force is ultimately limited by the dissipation in the cantilever and its temperature. We have pushed this limit by cooling a single-crystal silicon cantilever in vacuum to a temperature below 100 mK. To sense the sub-angstrom thermal-mechanical motion with minimal heating of the cantilever, an improved optical fiber interferometer was developed that could be operated at optical powers as low as 2 nW. The cantilever mean square amplitude of vibration showed the expected linear dependence on temperature down to 400 mK, at which point other noise sources became significant. At the lowest temperature, the cantilever achieved a noise temperature of 220 mK, with a corresponding force noise of 820 zeptonewtons in a 1 Hz bandwidth.