  We study the $\epsilon$-level sets of the signed distance function to a
planar Jordan curve $\Gamma$, and ask what properties of $\Gamma$ ensure that
the $\epsilon$-level sets are Jordan curves, or uniform quasicircles, or
uniform chord-arc curves for all sufficiently small $\epsilon$. Sufficient
conditions are given in term of a scaled invariant parameter for measuring the
local deviation of subarcs from their chords. The chordal conditions given are
sharp.
