Assuming all you did was bolt on a Biopace triple to replace a double crank of some kind (Shimano?). The most obvious answer would be not using the correct spindle length for a triple. Square taper cranks are all mated to a specific length spindle; in some cases a triple of one model will have a shorter spindle than a double of another..you said the chainline has the big chainring lining up between 6th and 7th gear. With a triple 8sp the chainline should line up the middle chainring between 4th and 5th (with the big chain ring probably between 5 and 6). With your being between 6-7, it seems to indicate your crankset is too far outboard by 3-5 mm (probably due to spindle that is too long). This could easy explain the chain being pulled of the big chain ring when in the lower gears (1-5). Also the big chainring may be beyond the range of the front derailleur, also resulting if the chian being pulled off the big chainring.

However I would also suggest you replace you chain as it has lengthened to the point I replace my chains.