The ${6s}^{2}^{1}S_{0}\ensuremath{\rightarrow}6s5d^{3}D_{1}$ transition in atomic Yb is proposed for use in the study of atomic parity nonconservation (PNC). This transition is shown to have a very large $E1$ amplitude arising from PNC: $|\mathrm{Im}({E1}_{\mathrm{PNC}})|\ensuremath{\cong}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}{\mathrm{ea}}_{0}$, and also a strongly suppressed $M1$ amplitude and a moderate Stark-induced amplitude. Extremely high-precision measurements of PNC in Yb appear possible, using experimental techniques of proven utility. Comparison of PNC in the wide range of stable isotopes of Yb may provide a unique test of the standard model of electroweak interactions.