It is possible to use Snapchat from a computer; however, you need to install the BlueStacks App Player to do so. The BlueStacks App player is an Android emulator software that allows you to use Android Applications from your computer.
BlueStacks merges your WIndows or OSX and Android experiences, allowing you to easily navigate between them. It is optimized for the mouse and keyboard, allowing you to both use messaging apps and play games. The player also features camera and microphone integration and lets you to share files directly from your PC or Mac to your mobile applications. BlueStacks can be downloaded from BlueStacks.com.