Alternator...probably internal voltage regulator or alternator diode went bad.
In any event, the earlier ones were component-replaceable. You may be looking at having to replace the entire alternator.
A charging system check would tell you a lot. With engine running and all non-essential accessories off, a check at the battery terminals should produce 13.5 - 14.4V. Outside of that range indicates a problem.
I replaced my alternator last year when I saw (and smelled) the battery venting...voltage output was 17.5V!!!
Dealer will charge $500 or more to replace the alternator...if you buy the part at FastLane, it's a DIY job at $250.