This paper presents the use of a generalized learning technique to automatically generate Bangla poetry. We have trained a Long Sort Term Memory (LSTM) based recurrent neural network model on 350 poems written by Rabindranath Tagore to inspect if the recurrent neural network learns to generate poems. Using the technique described in this paper, we are able to generate poems using seed texts provided as input. The generated poems display some interesting patterns, such as rhythm as well as limited semantic and emotional contexts. To the best of our knowledge, this is the first work on automatic Bengali poetry generation using such models.