The first battle of Clusium (82 BC) was an inconclusive battle between Sulla and Carbo, fought eighty miles to the north of Rome (Sulla's Second Civil War).
At the start of the campaign of 82 BC Gnaeus Papirius Carbo had moved north to deal with Sulla's ally Metellus Pius, and after an initial setback for one of his lieutenants on the Aesis River besieged Metellus somewhere in the north. However his colleague in the south, Marius the Younger, suffered a defeat at Sacriportus and had to take refuse in Praeneste, where he was besieged. This forced Carbo to abandon the campaign in the north, and return south. Sulla beat him to Rome, and the focus of the campaign then moved to the vicinity of Clusium, on the River Glanis, about 80 miles to the north of Rome.
Carbo had at least three separate forces north of Rome. He commanded the central force, which was around Clusium (modern Chiusi). His lieutenant Carinnas was approaching Spoletium, 40 miles to the east/ south-east of Clusium. Finally a detachment was at Saturnia, 35 miles to the south-west of Clusium. All three were on Roman roads - from west to east the Via Clodia, Via Cassia and Via Flaminia, all of which headed for Rome.
Sulla moved north from Rome to deal with the new threat, leaving his lieutenant Q. Lucretius Ofella in command of the siege of Praeneste. Appian places Sulla at three battles in a row, although their locations suggests that he was probably only in command at the first and third.
The first battle came on the River Glanis, presumably somewhere to the south of Clusium, where Sulla defeated a force of Celtiberian cavalrymen that had been sent from Spain to support the consuls. Next he is reported to have defeated a detachment of Carbo's men at Saturnia. Finally came the battle at Clusium. This seems like an unusual route, with Sulla zigzagging across the countryside, and leaving Carbo with his main army behind him while headed for Saturnia, so this second battle probably involved a separate detachment of Sulla's men.
The battle of Clusium lasted all day, and was only ended by darkness. The battle ended inconclusively, although the course of the rest of the campaign suggests that Carbo remained in position around Clusium, while Sulla withdrew a short distance.
The next action came at Spoletium, where Pompey defeated and besieged Carinnas. Carbo was still near enough to try and send a relief force, although this was defeated by troops sent by Sulla, demonstrating that he was also in the area. Carinnas managed to escape from Spoletium under cover of a storm. Carbo then sent Marcius to try and lift the siege of Praeneste, but this was ambushed by Pompey, and forced to retreat, suggesting that the four armies were still in the same area.
The situation was now changed by the Samnites, who raised a large army and attempted to lift the siege of Praeneste. This forced Sulla to dash south to block them. Pompey was probably left in the area around Clusium, as that is where he next appears, while Carbo made a dash north to try and catch Metellus Pius by surprise, but instead suffered a heavy defeat at Faventia.
Some of our other sources hint at a previous battle at Clusium. Velleius Paterculus gives a list of several victories won by Sulla's supporters just before the battle of Sacriportus, won by 'the two Servilii at Clusium, Metellus Pius at Faventia and Marcus Lucullus in the vicinity of Fidentia'. The battle of Faventia definitely happened after Sacriportus and we have no firm date for Fidentia. This might suggest that there was an early clash at Clusium, and Appian does record a Servilius as one of Sulla's successful generals. However it might also just be that Servilius fought at the known battle of Clusium.