  We predict a huge interference effect contributing to the conductance through
large ultra-clean quantum dots of chaotic shape. When a double-dot structure is
made such that the dots are the mirror-image of each other, constructive
interference can make a tunnel barrier located on the symmetry axis effectively
transparent. We show (via theoretical analysis and numerical simulation) that
this effect can be orders of magnitude larger than the well-known universal
conductance fluctuations and weak-localization (both less than a conductance
quantum). A small magnetic field destroys the effect, massively reducing the
double-dot conductance; thus a magnetic field detector is obtained, with a
similar sensitivity to a SQUID, but requiring no superconductors.
