  Interactions between cold ions and atoms have been proposed for use in
implementing quantum gates\cite{Idziaszek2007}, probing quantum
gases\cite{Sherkunov2009}, observing novel charge-transport
dynamics\cite{Cote2000}, and sympathetically cooling atomic and molecular
systems which cannot be laser cooled\cite{Smith2005,Hudson2009}. Furthermore,
the chemistry between cold ions and atoms is foundational to issues in modern
astrophysics, including the formation of stars, planets, and interstellar
clouds\cite{Smith1992}, the diffuse interstellar bands\cite{Reddy2010}, and the
post-recombination epoch of the early universe\cite{Stancil1996b}. However, as
pointed out in refs 9 and 10, both experimental data and a theoretical
description of the ion-atom interaction at low temperatures, reached in these
modern atomic physics experiments and the interstellar environment, are still
largely missing. Here we observe a chemical reaction between ultracold
$^{174}$Yb$^+$ ions and $^{40}$Ca atoms held in a hybrid trap. We measure, and
theoretically reproduce, a chemical reaction rate constant of $ \rm \bf K
=(2\pm1.3)\times10^{-10} cm^{3}s^{-1}$ for $ \rm \bf 1 mK \leq T \leq 10 K$,
four orders of magnitude higher than reported for other heteronuclear cases. We
also offer a possible explanation for the apparent contradiction between
typical theoretical predictions and measurements of the radiative association
process in this and other systems.
