I am searching for an Chrome extension by which I can play music saved in my local drive.
All I want is to play music from my computer without using any media player, but by using my browser only.
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Enjoy Music Player (this one also supports online music) or Achshar Player seem to do exactly what you want: play local music with Chrome, though I have not tested them myself. They also come with a neat music-browser, playlists and some more media player-features. They run offline in a separate window (Chrome App), so you don't even need to open Chrome itself.
If you don't want that, there's also MP3 Player by AntiMatter which runs online and supports searching for songs by name or artist and shuffling.