I assume you are talking about hot rolled structural steel.
According to the current 2005 AISC Spec, the allowable strength is FyZ/1.67, where 1.67 is the safety factor and Z is the minor axis plastic section modulus. This has to be less than 1.6FyS where S is the weak axis section modulus. According to the AISC BAsic Design Value Cards, the weak axis allowable strength for channels can be taken as .9FyS, where S is the weak axis section modulus. The design cards use equations that have been simplified from the Spec.
If you are using the 9th Edition AISC (green book), it's not explicitly given. Logiacally, you would expect at least the same allowable stress assuming a compact section because you won't have lateral torsional buckling. However, if you read section F2, the text says that 0.75Fy only applies for doubly symetrical I and H shapes. It was the practice of my office when we used the green book to only use .6Fy as the allowable stress for weak axis bending of channels. This is very conservative, but we didn't feel that the spec supported a higher value, although from a technical standpoint we knew it was much higher.