It is advisable to finish your story before you consider contacting an agent or publisher.
Agents and publishers are interested in manuscripts that look as professional and as polished as possible. An incomplete first draft manuscript that is incomplete is neither professional, nor polished.
For your writing to look professional, you will need to write and rewrite your work many times over. It is not the responsibility of an editor to correct spelling or grammatical errors. If you think your first draft will be free from these errors, think again. Even Jack Kerouac who supposedly wrote "On the Road" in three weeks had to go back and reedit his first draft to correct numerous mistakes. And Kerouac's prose is often as perfect as it gets.
If you are up to chapter three on the very first draft of your work, then there is a good chance that you work could turn out very differently to what you first thought. No matter how carefully you plot a novel, characters and situations can sometimes take a different shape once you begin to write them. You will not truly know what shape your work will take until you have completed your manuscript. You will also be unaware of other factors, such as word count, which can be important when pitching your novel to a publisher or agent.
The only writers who can get away with pitching an idea to a publisher are well established authors who have signed a contract to say that they will write several books (perhaps in a series) for that publisher. As you are not an established, best selling author, it is unlikely that a publisher would be interested in your plans.
My advice is to keep working. Maybe your idea is awesome. Maybe it will change the publishing industry as we know it. But for now, you need to concentrate on writing your book, not selling it.