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)=0.108 (GeV/c)(2) and at a forward electron scattering angle of 30 degrees <theta(e)<40 degrees . The measured asymmetry is A(LR)(e-->p)=[-1.36+/-0.29(stat)+/-0.13(syst)]x10(-6). The expectation from the standard model assuming no strangeness contribution to the vector current is A(0)=(-2.06+/-0.14)x10(-6). We have improved the statistical accuracy by a factor of 3 as compared to our previous measurements at a higher Q2. We have extracted the strangeness contribution to the electromagnetic form factors from our data to be G(s)(E)+0.106G(s)(M)=0.071+/-0.036 at Q(2)=0.108 (GeV/c)(2). We again find the value for G(s)(E)+0.106G(s)(M) to be positive, this time at an improved significance level of two sigma.