Comb-based optical arbitrary waveform measurement (OAWM) techniques can overcome the bandwidth limitations of conventional coherent detection schemes and may have disruptive impact on a wide range of scientific and industrial applications. Over the previous years, different OAWM schemes have been demonstrated, showing the performance and the application potential of the concept in laboratory experiments. However, these demonstrations still relied on discrete fiber-optic components or on combinations of discrete coherent receivers with integrated optical slicing filters that require complex tuning procedures to achieve the desired performance. In this paper, we demonstrate the first wavelength-agnostic OAWM front-end that is integrated on a compact silicon photonic chip and that neither requires slicing filters nor active controls. Our OAWM system comprises four IQ receivers, which are accurately calibrated using a femtosecond mode-locked laser and which offer a total acquisition bandwidth of 170 GHz. Using sinusoidal test signals, we measure a signal-to-noise-and-distortion ratio (SINAD) of 30 dB for the reconstructed signal, which corresponds to an effective number of bits (ENOB) of 4.7 bit, where the underlying electronic analog-to-digital converters (ADC) turn out to be the main limitation. The performance of the OAWM system is further demonstrated by receiving 64QAM data signals at symbol rates of up to 100 GBd, achieving constellation signal-to-noise ratios (CSNR) that are on par with those obtained for conventional coherent receivers. In a theoretical scalability analysis, we show that increasing the channel count of non-sliced OAWM systems can improve both the acquisition bandwidth and the signal quality. We believe that our work represents a key step towards out-of-lab use of highly compact OAWM systems that rely on chip-scale integrated optical front-ends.