We present phase shift measurements for neutron matter waves in vacuum and in low pressure Helium using a method originally developed for neutron scattering length measurements in neutron interferometry. We search for phase shifts associated with a coupling to scalar fields. We set stringent limits for a scalar chameleon field, a prominent quintessence dark energy candidate. We find that the coupling constant $beta$ is less than 1.9 $times10^7$~for $n=1$ at 95% confidence level, where $n$ is an input parameter of the self--interaction of the chameleon field $varphi$ inversely proportional to $varphi^n$.
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