Flukybot
Yes, you can run a Telegram bot locally in your own browser using JavaScript. No need to install anything since you already have a browser. You're not likely to have your browser online all the time though, so the bot might be a bit fluky. This is mainly a proof-of-concept and a way to experiment with the Bot API with JavaScript.
The example includes receiving messages, sending messages, custom keyboards and using the bot inline. You can easily use other parts of the Bot API using similar code.
You can try it out at kunal-diwan.github.io/flukybot/ or download the index.html file and open it locally.
Creating your own bot
If you are new to bots or bot development for Telegram check out the following links:
Introduction to bots Telegram Bot API documentation Bots FAQ