The number that matters is rated PTO HP, not engine HP. Tractors lose 10–15% between the crankshaft and the PTO shaft. A 35 HP engine tractor typically produces around 30 PTO HP — right at the minimum for an 8-inch hydraulic chipper.
Rough sizing rule: 3–4 PTO HP per inch of max branch diameter. A 4.5-inch chipper wants 15–20 PTO HP. A 6-inch chipper wants 25–30 PTO HP. An 8-inch chipper wants 30–40 PTO HP. A 9-inch commercial unit wants 45+ PTO HP.
Also check your tractor’s 3-point hitch lift capacity. An 8-inch chipper weighs 1,100–1,400 lb; a 9-inch commercial unit pushes 1,600 lb.