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We present ALMA 850 $\mu$m continuum observations of the Orion Nebula Clusterthat provide the highest angular resolution ($\sim 0\rlap{.}''1 \approx 40$ AU)and deepest sensitivity ($\sim 0.1$ mJy) of the region to date. We mosaicked afield containing $\sim 225$ optical or near-IR-identified young stars, $\sim60$ of which are also optically-identified "proplyds". We detect continuumemission at 850 $\mu$m towards $\sim 80$% of the proplyd sample, and $\sim 50$%of the larger sample of previously-identified cluster members. Detected objectshave fluxes of $\sim 0.5$-80 mJy. We remove sub-mm flux due to free-freeemission in some objects, leaving a sample of sources detected in dustemission. Under standard assumptions of isothermal, optically thin disks,sub-mm fluxes correspond to dust masses of $\sim 0.5$ to 80 Earth masses. Wemeasure the distribution of disk sizes, and find that disks in this region areparticularly compact. Such compact disks are likely to be significantlyoptically thick. The distributions of sub-mm flux and inferred disk sizeindicate smaller, lower-flux disks than in lower-density star-forming regionsof similar age. Measured disk flux is correlated weakly with stellar mass,contrary to studies in other star forming regions that found steepercorrelations. We find a correlation between disk flux and distance from themassive star $\theta^1$ Ori C, suggesting that disk properties in this regionare influenced strongly by the rich cluster environment.

Protoplanetary Disk Properties in the Orion Nebula Cluster: Initial Results from Deep, High-Resolution ALMA Observations