This paper focuses on channel estimation for mmWave MIMO systems with 1-bit spatial sigma-delta analog-to-digital converters (ADCs). The channel estimation performance with 1-bit spatial sigma-delta ADCs depends on the quantization noise modeling. Therefore, we present a new method for modeling the quantization noise by leveraging the deterministic input-output relation of the 1-bit spatial sigma-delta ADC. Using this new noise model, we propose an algorithm for channel estimation for a narrowband single-user mmWave line-of-sight MIMO system by determining the unknown angles and path attenuation that characterize the flat fading channel. Through simulations, we demonstrate that the performance of the developed method is comparable to the traditional analog systems and significantly better than the conventional 1-bit quantized systems.