I have annotated the game Goeller - Camenares, Correspondence 2011, where I had the chance to learn more about the Chekhover Sicilian (B53) played via the relatively unusual move order 1.e4 c5 2.Nc3 d6 3.d4!? exd4 4.Qxd4 (see diagram above). Though I ended up transposing to the main Chekhover lines popularized by Evgeni Vasiukov, I was inspired by the way Gadimir Guseinov plays the line with an early f4 (made possible by avoiding Nf3 right away), as described in my notes. This line is sometimes called "the Hungarian Variation," but much more often named after Vitaly Chekhover (1908-1965), who seems to have originated it in the game Chekhover - Lisitsin, Leningrad 1938 (though I could find no other examples of his playing it). He is best remembered today as an endgame composer and writer and was a professional musician and pianist.
The opening variation (which usually arises by 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Qxd4) is fairly popular among amateurs, since it allows free and rapid development of the pieces in the style of Paul Morphy and even resembles Morphy's approach to the Philidor as White with 1.e4 e5 2.Nf3 d6 3.d4 exd4 4.Qxd4. Though it is possible to play the line with an early c4 advance, seeking control over the center in Maroczy-bind fashion, it is much more common among amateurs simply to develop the pieces to natural squares by Nf3, Nc3, Qd4, Bb5, Bg5, O-O-O, and Rhe1 with complete mobilization and free play in the center. White will later retreat his Queen to d3 or d2 and centralize the Knight with Nd4 as a prelude to a kingside attack with f3 or f4, g4, and h4 etc. I have always been impressed by how naturally rapid development leads to an attack in this line, especially in Vasiukov's games (which are featured in my notes). However, it is generally not difficult for Black to find counterplay if he knows what he is doing and is willing to take some risks. After close analysis, I think the line is basically equal, with chances for both sides, but that does not make it less interesting to play!
For those who want to learn more about the Chekhover (sometimes spelled Checkhover online), I have put together a brief webliography of sources. There is an excellent video by GM Ronen Har-Zvi put out by ICC (see preview). You can find a large number of videos on YouTube that set forth a repertoire based on this line, though I have only embedded those where White plays Nc3 rather than the Maroczy idea of c4 (you can find the rest of his videos easily enough if that interests you). Pete Tamburro had some lectures a while back at ChessFM/ICC on the Chekhover in his "Openings for Amateurs" series, though I cannot locate them now (and they would only be available for subscribers anyway). Those interested in having a book might consider A Startling Chess Opening Repertoire by Chris Baker, though I express some reservations about his recommendations in my notes.
Sicilian (B53) and Sicilian B53 Best Games at Chessgames
A useful collection of Chekhover Sicilian games and a great compilation of "best games" to help you get a quick sense of ideas and themes in this line. You might also search games of Vasiukov playing Sicilian B53 for more inspiration.
ECO B53: Sicilian, Chekhover Variation from 365Chess
Another useful games collection for getting a quick overview, though this one does not allow you to download files without subscription.
Vasiukov - Van Wely, Aeroflot 2002 annotated by Boris Schipkov
This is one of the nicest games for White in this line, very well annotated at the Chess Siberia site.
Strictly for Amateurs by Bobby Ang
A nice introduction to the line and apparently Ang's first published chess writing. But he later wrote an even better one on the Chekhover in his "Chess Pieces" series that I cannot locate. From the Internet Archives.
Opening Lanes #15 by Gary Lane
Discusses issues with the early e5 advance by White (which is advocated by Chris Baker).
Sicilian Checkhover Variation: A Diamond in the Rough at Chess.com
Warning: this page kept crashing my browser (which likely needs updating). Focuses on the games of Judit Polgar with the line.
La Variante Chekhover by Francisco Acosta Ruiz
From the defunct Hechiceros site, via the internet archives. This article offers an interesting approach for Black to the Maroczy bind with c4 by playing an early f5. I include this only because it would likely be hard to find -- and to give you one more reason to reject c4 ideas.