Bilingual lexicons and phrase tables are critical resources for modern Machine Translation systems. Although recent results show that without any seed lexicon or parallel data, highly accurate bilingual lexicons can be learned using unsupervised methods, such methods rely on the existence of large, clean monolingual corpora. In this work, we utilize a single Skip-gram model trained on a multilingual corpus yielding polyglot word embeddings, and present a novel finding that a surprisingly simple constrained nearest-neighbor sampling technique in this embedding space can retrieve bilingual lexicons, even in harsh social media data sets predominantly written in English and Romanized Hindi and often exhibiting code switching. Our method does not require monolingual corpora, seed lexicons, or any other such resources. Additionally, across three European language pairs, we observe that polyglot word embeddings indeed learn a rich semantic representation of words and substantial bilingual lexicons can be retrieved using our constrained nearest neighbor sampling. We investigate potential reasons and downstream applications in settings spanning both clean texts and noisy social media data sets, and in both resource-rich and under-resourced language pairs.