We present a benchmark for Planning And Reasoning Tasks in humaN-Robot collaboration (PARTNR) designed to study human-robot coordination in household activities. PARTNR tasks exhibit characteristics of everyday tasks, such as spatial, temporal, and heterogeneous agent capability constraints. We employ a semi-automated task generation pipeline using Large Language Models (LLMs), incorporating simulation-in-the-loop for the grounding and verification. PARTNR stands as the largest benchmark of its kind, comprising 100,000 natural language tasks, spanning 60 houses and 5,819 unique objects. We analyze state-of-the-art LLMs on PARTNR tasks, across the axes of planning, perception and skill execution. The analysis reveals significant limitations in SoTA models, such as poor coordination and failures in task tracking and recovery from errors. When LLMs are paired with 'real' humans, they require 1.5x as many steps as two humans collaborating and 1.1x more steps than a single human, underscoring the potential for improvement in these models. We further show that fine-tuning smaller LLMs with planning data can achieve performance on par with models 9 times larger, while being 8.6x faster at inference. Overall, PARTNR highlights significant challenges facing collaborative embodied agents and aims to drive research in this direction.