This is a nuanced situation. Doubling Season's effect doubles counters placed on permanents you control. However, the loyalty counters a planeswalker enters with are not 'placed' by a spell or ability in the usual sense — they are set as part of the planeswalker's characteristic definition as it enters the battlefield.
According to CR 306.5b, a planeswalker enters the battlefield with a number of loyalty counters equal to its printed loyalty value. This is a characteristic-defining action that establishes the planeswalker's initial state, not a 'placing' of counters triggered by a spell or ability. The Oracle ruling and official judge consensus confirm Doubling Season does NOT apply here.
Wait — this answer requires a correction based on actual official rulings. The official Gatherer ruling on Doubling Season explicitly states that it does affect loyalty counters placed on a planeswalker as it enters the battlefield. CR 614.1c covers replacement effects that modify how permanents enter, and Doubling Season creates such a replacement effect (CR 614.1c) that applies as the planeswalker enters with its counters.
So the correct verdict is: Yes, Doubling Season does double the loyalty counters a planeswalker enters with, because its replacement effect (CR 614.1c) applies to counters placed on permanents as they enter, and the loyalty counters placed as a planeswalker enters fall under this replacement effect.
Example: You control Doubling Season and cast Chandra, Torch of Defiance (printed loyalty 4). As she enters the battlefield, the replacement effect of Doubling Season doubles the 4 counters to 8, meaning she enters with 8 loyalty counters. You can then immediately activate a loyalty ability costing −X if your 8 counters are sufficient.
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.