Graph Neural Networks (GNNs) have received significant attention recently, but training them at a large scale remains a challenge.Mini-batch training coupled with sampling is used to alleviate this challenge.However, existing approaches either suffer from the neighborhood explosion phenomenon or have suboptimal performance. To address these issues, we propose a new sampling algorithm called LAyer-neighBOR sampling (LABOR). It is designed to be a direct replacement for Neighbor Sampling (NS) with the same fanout hyperparameter while sampling up to 7 times fewer vertices, without sacrificing quality.By design, the variance of the estimator of each vertex matches NS from the point of view of a single vertex.Moreover, under the same vertex sampling budget constraints, LABOR converges faster than existing layer sampling approaches and can use up to 112 times larger batch sizes compared to NS.