Recently a number of algorithms under the theme of 'unbiased learning-to-rank' have been proposed, which can reduce position bias, the major type of bias in click data, and train a high-performance ranker with click data. Most of the existing algorithms, based on the inverse propensity weighting (IPW) principle, first estimate the click bias at each position, and then train an unbiased ranker with the estimated biases using a learning-to-rank algorithm. However, there has not been a method for unbiased pairwise learning-to-rank that can simultaneously conduct debiasing of click data and training of a ranker using a pairwise loss function. In this paper, we propose a novel framework to accomplish the goal and apply this framework to the state-of-the-art pairwise learning-to-rank algorithm, LambdaMART. Our algorithm named Unbiased LambdaMART can jointly estimate the biases at click positions and the biases at unclick positions, and learn an unbiased ranker. Experiments on benchmark data show that Unbiased LambdaMART can significantly outperform existing algorithms by large margins. In addition, an online A/B Testing at a commercial search engine shows that Unbiased LambdaMART can effectively conduct debiasing of click data and enhance relevance ranking.