Recent numerical results point to the existence of a conformally invariant
twist defect in the critical 3d Ising model. In this note we show that this
fact is supported by both epsilon expansion and conformal bootstrap
calculations. We find that our results are in good agreement with the numerical
data. We also make new predictions for operator dimensions and OPE coefficients
from the bootstrap approach. In the process we derive universal bounds on
one-dimensional conformal field theories and conformal line defects.