Who among the following was the founder of the Chalukya dynasty?

Concept: A dynasty’s "founder" is the ruler who first established independent sovereign authority for that house — he breaks away from an overlord, fixes a capital, and assumes imperial titles — rather than a later descendant who merely expanded an already sovereign kingdom. "Chalukya" also names three distinct lines, so the founder question must be settled for the earliest, parent line: the Chalukyas of Vatapi (Badami) in the Deccan.

Application: The Badami (Early Western) Chalukya house was established by Pulakeshin I around 543 CE. He was the first of the line to declare independence from the Kadambas, fortified the hill site of Vatapi (modern Badami, Bagalkot district, Karnataka) as his capital, and performed the Ashvamedha sacrifice — the classical proclamation of paramount, independent kingship. The Badami cave-and-cliff inscription of 543 CE records this foundation, which is why every later Chalukya ruler is reckoned as his successor.

Cross-check — placing the other names in the same lineage:

• Kirtivarman I (c. 566–598 CE) — son of the founder; he conquered the Nalas, Mauryas of Konkan and Kadambas and is called the "first creator of Vatapi" for its embellishment, but he inherited an already independent kingdom.

• Vikramaditya I (c. 654–681 CE) — the founder’s great-grandson, ruling three generations later; his achievement was restoring Chalukya power after the Pallava occupation of Vatapi, i.e. a revival within an already established dynasty.

• Rajendra II (11th century CE) — a Chola king of the Tamil country, of a rival southern house altogether, not a Chalukya ruler at all.

Result: Independent sovereignty for the Chalukya house begins with Pulakeshin I, c. 543 CE, at Vatapi — so he is the founder of the dynasty.