  The collision of a fixed point with a switching manifold (or border) in a
piecewise-smooth map can create many different types of invariant sets. This
paper explores two techniques that, combined, establish a chaotic attractor is
created in a border-collision bifurcation in $\mathbb{R}^d$ $(d \ge 1)$. First,
asymptotic stability of the fixed point at the bifurcation is characterised and
shown to imply a local attractor is created. Second, a lower bound on the
maximal Lyapunov exponent is obtained from the determinants of the one-sided
Jacobian matrices associated with the fixed point. Special care is taken to
accommodate points whose forward orbits intersect the switching manifold as
such intersections can have a stabilising effect. The results are applied to
the two-dimensional border-collision normal form focusing on parameter values
for which the map is piecewise area-expanding.
