A quantum critical point (QCP) occurs upon chemical doping of the weak itinerant ferromagnet Sc3.1In. Remarkable for a system with no local moments, the QCP is accompanied by non-Fermi liquid behavior, manifested in the logarithmic divergence of the specific heat both in the ferro-and the paramagnetic states, as well as linear temperature dependence of the low-temperature resistivity. With doping, critical scaling is observed close to the QCP, as the critical exponents δ, γ, and β have weak composition dependence, with δ nearly twice and β almost half of their respective mean-field values. The unusually large paramagnetic moment μPM∼1.3μB/F.U. is nearly composition independent. Evidence for strong spin fluctuations, accompanying the QCP at xc=0.035±0.005, may be ascribed to the reduced dimensionality of Sc3.1In, associated with the nearly one-dimensional Sc-In chains.