Athirajendra Chola
Athirajendra Chola (1070 CE) reigned for a very short period of few months as the Chola king succeeding his father Virarajendra Chola.
His reign was marked by civil unrest, possibly religious in nature.
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Virarajendra Chola
Virarajendra Chola (r.1063–1070 CE) is considered to be one of the most underrated Chola kings, mainly because a major part of his life was spent as a subordinate of his two elder brothers Rajadhiraja Chola I and Rajendra Chola II, who along with Virarajendra Chola himself were the illustrious sons of their Chakravarti(Emperor) father, Rajendra Chola I.
While certainly it was not a practice among the Chola kings to nominate the eldest son, but the most capable (in administration of their domains as well as proving their mettle on the battlefield) as the heir to the throne.
During his early reign he granted the maintenance of a school to study the Vedas, Sastras and Grammar and a hostel was provided for the students.
A hospital named Virasolan was also provided by him for the sick people.
The famous grammatical work in Tamil, Virasoliyam was written by Buddhamitra during his reign.
Virarajendra’s reign falls in a period of the medieval Cholas, when it was both trying to expand its boundaries and preserve its existing territories, but had appeared to stutter in its attempts because of the death, in his prime, of the eldest brother and king Rajadhiraja-I and the short rule of Virarajendra's elder brother Rajendra-II.
In total, the three brothers ruled for 16-20 years altogether by succeeding one another.
This rapid succession was seen as a golden opportunity by the traditional enemies and subordinates of the Cholas, viz.
the Singhalas (Ceylon), Western Chalukya Empire, Pandyas and even the Cheras, with each adversary either trying to become free or declaring a war on the Cholas.
Ultimately, however, Virarajendra proved to be a very capable and brave ruler, who was kind and protective to his subjects, reimposed authority on Chola dominions and was particularly ruthless to the old nemeses of the Cholas, both the Chalukyas and the Pandyas.
Viewed overall, especially in the context of the fact that his own rule lasted for less than 10 years, yet, as borne out by his various inscriptions in Karur, Virarajendra's was a lasting legacy in that in the short time he ruled, he overwhelmed everyone of his adversaries, and succeeded not only in preserving Chola territories, but also made overseas concquests in far-off lands like Indonesia, Malaysia, Sri Lanka, Nicobar, Sakkarakottam (around Bastar district, Chhattisgarh - this was also a place governed by the next major Chola monarch, Kulothunga-I or Rajendra Chalukya, son of Eastern Chalukya King Rajaraja Narendra and thus grandson of Rajendra Chola I through his daughter Ammangadevi.

Question: Who is Athirajendra Chola's paternal grandfather?
Answer: Rajendra Chola I