We propose a novel regularized adaptation technique for context dependent deep neural network hidden Markov models (CD-DNNHMMs). The CD-DNN-HMM has a large output layer and many large hidden layers, each with thousands of neurons. The huge number of parameters in the CD-DNN-HMM makes adaptation a challenging task, esp. when the adaptation set is small. The technique developed in this paper adapts the model conservatively by forcing the senone distribution estimated from the adapted model to be close to that from the unadapted model. This constraint is realized by adding KullbackÔÇôLeibler divergence (KLD) regularization to the adaptation criterion. We show that applying this regularization is equivalent to changing the target distribution in the conventional backpropagation algorithm. Experiments on Xbox voice search, short message dictation, and Switchboard and lecture speech transcription tasks demonstrate that the proposed adaptation technique can provide 2%-30% relative error reduction against the already very strong speaker independent CD-DNN-HMM systems using different adaptation sets under both supervised and unsupervised adaptation setups.