The Chameleon class has both the Arcane Focus and Divine Focus class features which allows a character to cast Arcane spells and Divine spells respectively.
It is explicit that:
You can't use any abilities gained from your aptitude focus, ability boon, or mimic class feature abilities to qualify for a feat, prestige class, or other option.
So, in general, it takes another class to grant entry into another Prestige Class which progresses spellcasting (though some, like Human Paragon, could be entered with no fuss).
Also, the Caster Level of a Chameleon is somewhat special, for both Arcane Focus and Divine Focus:
Your caster level is equal to twice your class level.1
Let's focus on two specific prestige classes, selected because they are freely available online, and assume that the requirements are fulfilled by other means:
The former says:
At 2nd and 3rd level, a human paragon gains new spells per day (and spells known, if applicable) as if he had also gained a level in a spellcasting class he belonged to before adding the level. He does not, however, gain any other benefit a character of that class would have gained (bonus metamagic or item creation feats, bard or assassin abilities, and so on). This essentially means that he adds the level of human paragon to the level in the spellcasting class, then determines spells per day, spells known, and caster level accordingly.
If a character had more than one spellcasting class before he became a human paragon, he must decide to which class he adds each level of human paragon. If a human paragon has no levels in a spellcasting class, this class feature has no effect.
And the latter:
At each level, a Fochlucan lyrist gains new spells per day (and spells known, if applicable) as if she had also gained a level in any one arcane spellcasting class and any one divine spellcasting class to which she belonged before adding the prestige class level. She does not, however, gain any other benefit a character of that class would have gained. If she had more than one arcane spellcasting class or divine spellcasting class before becoming a Fochlucan lyrist, she must decide to which class to add each Fochlucan lyrist level for the purpose of determining spells per day, spells known, and overall caster level.
Which brings the following questions:
- Is the Chameleon considered a spellcasting class, an arcane spellcasting class and/or a divine spellcasting class?2
- Can a single level of Fochlucan Lyrist advance Chameleon spellcasting twice (1 for Arcane, 1 for Divine)?3
- When advancing Chameleon spellcasting by one level, does the Caster Level progress by one or two levels?4
Thus, would a X 3/Chameleon 7/Fochlucan Lyrist 10 have:
- 27 levels of Chameleons for the purpose of spellcasting,
- Thus access to spells as a Chameleon 10 (progression stops there),
- And a Caster Level of 54 pre-items/feats?
1 Am I the only one smelling CL abuse here? Especially as Chameleon can be entered without any shenanigan at level 6?
2 I would tend to say Yes to all, in so far as being a spellcasting class seems informally defined as being able to cast spells.
3 It seems no dual spellcasting PrC's author ever thought that a single spellcasting class could qualify for both sides of the PrC.
4 The spellcasting progression seems unambiguous: a level is added to the spellcasting class to determine spells per day, spells known and caster level; and gaining one level of Chameleon raises Caster Level by 2.