Can you? Is it possible to use Two-weapon fighting melee combined with two weapon fighting ballistic to use both a chainsword and bolt pistol in close combat?

Yes, pistols may be used.

Actually, pistols are the only ranged weapon that may shot in melee.

When shooting, use BS to hit, and there is no range modifier (sorry, no +30 to hit, when in melee at least).

Also, they may be used with two weapon wielder/swift/lightning attack, read under those talents, but effectively:

-You get up to max attacks with melee weapon

-1 shot with pistol

(not multiple attacks with pistol, 1 attack with melee).

Also, yes, dual pistols may be used, but things like swift/lightning attack don't effect that.

EDIT: I'm also reasonably sure you can't semi/full auto if using the multiple attacks two weapons option (so no melee + multiple gunshots). I may be wrong though, so can someone else get this?

Reading over the book and reviewing my answer

KommissarK said:

The restriction you refer to is that in swift attack or lightning attacks- you must always apply the bonus to a single melee weapon, not both, and never on a gun (assuming you are using a melee weapon and a gun).

With a multiple attack action, under the Two-Weapon fighting it says that you make an attack with in melee combat each weapon if he is armed with a melee weapon in one hand and a pistol in the other. Regularly, if wielding a two weapons and one, or both are guns the character is able to full auto- or semi auto for the fire types even though he is wielding two weapons.

However, if he is using multiple attacks in melee according to pg. 140, Pistol weapons are fired one-handed and can be used to make a standard attack while engaged in melee (as you mentioned, disregarding any normal bonuses). Even though according to two weapon fighting you can fire the pistol on any mode, I'd imagine that being in melee restricts it to only being a standard attack.