  We report on a measurement of the parity violating asymmetry in the elastic
scattering of polarized electrons off unpolarized protons with the A4 apparatus
at MAMI in Mainz at a four momentum transfer value of $Q^2$ = \Qsquare
(GeV/c)$^2$ and at a forward electron scattering angle of 30$^\circ < \theta_e
< 40^\circ$. The measured asymmetry is $A_{LR}(\vec{e}p)$ = (\Aphys $\pm$
\Deltastat$_{stat}$ $\pm$ \Deltasyst$_{syst}$) $\times$ 10$^{-6}$. The
expectation from the Standard Model assuming no strangeness contribution to the
vector current is A$_0$ = (\Azero $\pm$ \DeltaAzero) $\times$ 10$^{-6}$. We
have improved the statistical accuracy by a factor of 3 as compared to our
previous measurements at a higher $Q^2$. We have extracted the strangeness
contribution to the electromagnetic form factors from our data to be $G_E^s$ +
\FakGMs $G_M^s$ = \GEsGMs $\pm $ \DeltaGEsGMs at $Q^2$ = \Qsquare (GeV/c)$^2$.
As in our previous measurement at higher momentum transfer for $G_E^s$ + 0.230
$G_M^s$, we again find the value for $G_E^s$ + \FakGMs $G_M^s$ to be positive,
this time at an improved significance level of 2 $\sigma$.
