Other circumstantial evidence suggests that the Saxon King Cearl of Mercia was involved (not sure on which side), simply because Mercia's influence and activities disappears from records until King Penda in 633.
Why Æthelfrith attacked is unknown. Geoffrey of Monmouth and Reginald of Durham, writing hundreds of years later, say that Æthelfrith wanted to find a rival hiding in Gwynedd, but there's no real evidence for this.
Bede and the Anglo-Saxon Chronicle give motivation for the attack to St. Augustine of Canterbury's calling down of divine vengeance on the local bishops a few years earlier, who did not support him in his mission to convert England to Christianity. (He was bringing Roman practices, trying to replace the local practices.)
Coincidentally (?), Bede may have been right, and here's why: there was a monastery nearby, at Bangor-on-Dee. Knowing that the battle was brewing (it took time for armies to arrive and assemble before the fighting actually started), several monks fasted for three days, then climbed a hill to observe the battle and pray for the defeat of Northumbria. Æthelfrith had them slaughtered. Bede says only 50 of 1200 escaped. The Anglo-Saxon Chronicle offers a more reasonable tally of 200 priests slain. Whatever the number, some saw this as the result of Augustine's rejection by the Briton bishops. (Odd that a pagan king would strike so far outside of his realm to be the tool of Christian judgment.)
Lots of questions about the Battle of Chester remain. We really don't know why it was fought, or all the significant figures who died. Various writers view it through their own Roman Christian bias. One of them, Geoffrey of Monmouth, deserves a closer look, which he will get tomorrow.