  The use of interferometric nulling for the direct characterization of
extrasolar planets is an exciting prospect, but one that faces many practical
challenges when deployed on telescopes. The largest limitation is the extreme
sensitivity of nullers to any residual optical path differences between the
incoming telescope beams even after adaptive optics or fringe-tracker
correction. The recently proposed kernel-nulling architecture attempts to
alleviate this by producing the destructive interference required for nulling,
in a scheme whereby self-calibrated observables can be created efficiently, in
effect canceling out residual atmospheric piston terms. Here we experimentally
demonstrate for the first time a successful creation of self-calibrated
kernel-null observables for nulling interferometry in the laboratory. We
achieved this through the use of a purpose-built photonic integrated device,
containing a multimode interference coupler that creates one bright, and two
nulled outputs when injected with three co-phased telescope beams. The device
produces the nulled outputs in a way that, by the subtraction of the measured
output flux, create a single self-calibrated kernel-null. We experimentally
demonstrate the extraction of kernel-nulls for up to 200 nm induced piston
error using a laboratory test-bench at a wavelength of 1.55 {\mu}m. Further, we
empirically demonstrate the kernel-null behaviour when injected with a binary
companion analogue equivalent to a 2.32 mas separation at a contrast of
10^{-2}, under 100 nm RMS upstream piston residuals.
