Should Lord of the Rings: The Two Towers be read in chronology?

I have the third book, Return of the King, which gives a time line of the events. But I just feel that splitting the book in half as JRR Tolkien does takes away from the story, i'd rather read Sam and Frodos quest mixed in with all the others. The Two Towers is split into two parts, Book 3 and Book 4. Book 3 is all about, well, everyone besides Frodo and Sam. I'm not saying I want to read TTT first before any of the other volumes, I'm just asking what are everyones thoughts on reading the book in the chronology order that the movie is in. So basically after every few chapters of book 3 i'd read some of Frodos chapters in book 4. Is that better, or would that take away from the story? Thoughts and/or ideas?