  In the Euclidean plane, two intersecting circles or two circles which are
tangent to each other clearly do not carry a finite Steiner chain. However, in
this paper we will show that such exotic Steiner chains exist in finite
Miquelian M\"obius planes of odd order. We state and prove explicit conditions
in terms of the order of the plane and the capacitance of the two carrier
circles $C_1$ and $C_2$ for the existence, length, and number of Steiner chains
carried by $C_1$ and $C_2$.
