  We present a novel method to constrain the mass of ultra-light bosons as the
dark matter using stellar streams formed by disrupting Globular Clusters in the
Milky Way. The turbulent density field of Fuzzy Dark Matter (FDM) haloes
results in perturbations and dynamical heating of thin streams. Using numerical
simulations based on an effective model, we explore the magnitude of this
phenomenon and show that this is observable for the range of axion masses $m_a$
that is interesting for alleviating the `small-scale problems' of $\Lambda$CDM.
We derive an analytical model for the thickening of thin stellar streams and
obtain an early conservative lower limit for the boson mass of $m_a > 1.5
\times 10^{-22}~$eV, using pre-Gaia literature data for six Milky Way streams
and after marginalizing over physical parameters. This demonstrates the great
promise for using this novel dynamical method as a fully independent probe of
FDM, to complement results based on Lyman-$\alpha$ forest data.
