Some early reports are that incorporation looks likely (with some restrictions) based on the "Due Process Clause" of the 14th Amendment.

Complete bans look unlikely to meet the "reasonable restriction" test. I'm guessing that when the opinion comes out in June or so, that Chicago will have to give up it's gun ban.

Analysis: 2nd Amendment Extension Likely (must read in its entirety)

In Chicago Gun Case, Supreme Court Sounds Note of Caution

Brady Campaign Statement

NRA Statement

Should be a transcript of the oral arguments released later. I'll link it here as an update when it comes out.

UPDATE - Oral Argument Transcript

Bonus reading

Using Guns to Protect Liberty

Chicagoans hope stories will help overturn gun ban

McDonald v. City of Chicago: Reading the Tea Leaves

Visual History of the SCOTUS.