In semiconductor device manufacturing, optical overlay metrology measures pattern placement between two layers in a chip with sub-nm precision. Continuous improvements in overlay metrology are needed to keep up with shrinking device dimensions in modern chips. We present first overlay metrology results using a novel off-axis dark-field digital holographic microscopy concept that acquires multiple holograms in parallel by angular multiplexing. We show that this concept reduces the impact of source intensity fluctuations on the noise in the measured overlay. With our setup we achieved an overlay reproducibility of 0.13 nm and measurements on overlay targets with known programmed overlay values showed good linearity of R2= 0.9993. Our data show potential for significant improvement and that digital holographic microscopy is a promising technique for future overlay metrology tools.