Both pronunciations are in use (depending on regional dialect). The standard pronunciation is nasalising the 'a'.
Also, चाँद comes from the Sanskrit चंद्र - 'chandra' (where the 'n' is pronounced). A Hindi synonym of चाँद which comes from the same root is चंद्रमा (where the 'n' is pronounced). So, you can imagine how a lot of people just end up pronouncing चाँद with the 'n'.
A similar thing happens with दाँत which comes from the Sanskrit दंत. Newly coined Hindi words like दंतमंजन (dantmañjan) - 'toothpaste' are derived from the Sanskrit word and have a nasal consonant.