  We report the first direct observation of collective quantum fluctuations in
a continuous field. Shot-to-shot atom number fluctuations in small sub-volumes
of a weakly interacting ultracold atomic 1D cloud are studied using \textit{in
situ} absorption imaging and statistical analysis of the density profiles. In
the cloud centers, well in the \textit{quantum quasicondensate} regime, the
ratio of chemical potential to thermal energy is $\mu/ k_B T\simeq4$, and,
owing to high resolution, up to 20% of the microscopically observed
fluctuations are quantum phonons. Within a non-local analysis at variable
observation length, we observe a clear deviation from a classical field
prediction, which reveals the emergence of dominant quantum fluctuations at
short length scales, as the thermodynamic limit breaks down.
