We propose a simple approach which, given distributed computing resources, can nearly achieve the accuracy of $k$-NN prediction, while matching (or improving) the faster prediction time of $1$-NN. The approach consists of aggregating denoised $1$-NN predictors over a small number of distributed subsamples. We show, both theoretically and experimentally, that small subsample sizes suffice to attain similar performance as $k$-NN, without sacrificing the computational efficiency of $1$-NN.