  Low frequency high precision laser interferometry is subject to excess
laser-frequency-noise coupling via arm-length differences which is commonly
mitigated by locking the frequency to a stable reference system. This approach
is crucial to achieve picometer level sensitivities in the 0.1 mHz to 1 Hz
regime, where laser frequency noise is usually high and couples into the
measurement phase via arm-length mismatches in the interferometers. Here we
describe the results achieved by frequency stabilising an external cavity diode
laser to a quasi-monolithic unequal arm-length Mach-Zehnder interferometer read
out at mid-fringe via balanced detection. We find this stabilization scheme to
be an elegant solution combining a minimal number of optical components, no
additional laser modulations and relatively low frequency noise levels. The
Mach-Zehnder interferometer has been designed and constructed to minimize the
influence of thermal couplings and to reduce undesired stray light using the
optical simulation tool ifocad. We achieve frequency-noise levels below 100
Hz/$\sqrt{\textrm{Hz}}$ at 1 Hz and are able to demonstrate the LISA frequency
prestabilization requirement of 300 Hz/$\sqrt{\textrm{Hz}}$ down to frequencies
of 100 mHz by beating the stabilized laser with an iodine-locked reference.
