  We report on signatures of classical chaos in ultracold collisions between a
trapped ion and a free atom. Using numerical simulations, we show that the
scattering dynamics can be highly sensitive to initial conditions for various
mass ratios and trapping frequencies, indicating the onset of chaos. We
quantify this chaotic dynamics by calculating its fractal dimension. We show
that for a trapped $^{88}$Sr$^+$ ion and a free $^{87}$Rb atom chaotic dynamic
appears under experimentally relevant conditions, and find its characteristic
energy scale. The observation of classical chaos in atom-trapped-ion collisions
suggests that signatures of quantum chaos might appear, for example, through a
Wigner-Dyson distribution of collisional resonances.
