Here's the list of possibilities: too little light, too much water, not enough water, too many leaves pinched off...

FataMorgana

LOL Fata. (Though absolutely correct.)

Seleur -- I'd water it. The soil should be nicely moist -- not wet -- and it should be receiving full light/sun. I'm going to GUESS that it's a wee bit late for this plant, but stranger things have happened.

If you give it a full watering, then let it sit out in the sun...see what happens. If it comes back -- great. If not -- so long as you have the light to offer a basil plant in your home (as it looks like you're doing this indoors?) -- go buy another and try again. I'd suggest.