Supernova explosion nearby A nearby star has crossed Chandrasekhar's limit. How do we come to know when it will undergo supernova explosion? 
Or has it already undergone supernova explosion?
The Chandrasekhar limit applies only for white dwarfs. Stars on the main sequence (or even off the main sequence) can easily surpass it, but if a white dwarf's mass is greater than the Chandrasekhar limit ($1.39 M_{\odot}$), it will undergo some sort of collapse.

First, though, in response to


  Or has it already undergone supernova explosion?


White dwarfs are not formed from supernovae, but from stars that (relatively) gently shed their outer layers to form planetary nebulae. So no, the stellar remnant will not have gone supernova already.

Back to the main question. If a white dwarf exists, its mass is less than the Chandrasekhar limit. To surpass that, it needs to gain mass. This can happen in binary systems where the white dwarf accretes matter from the more massive star (generally a giant). The white dwarf can then undergo a Type Ia supernova and explode. The light curve will look a bit like this:



A second (but far less likely) scenario is that two white dwarfs merge. The result? A Type Ia supernova and, possibly, a neutron star.