Step 1: Recall the context.
Kerala has been at the forefront of digital literacy initiatives in India, with several panchayats striving to become fully digitally literate.
Step 2: Identify the first digitally literate panchayat.
Pullampara Grama Panchayat in Thiruvananthapuram district became the first fully digitally literate panchayat in Kerala, with every household having at least one member trained in basic digital skills.
Step 3: Rule out other options.
Karukutty, Vellanad, and Nilambur are notable panchayats in Kerala but do not hold this specific distinction.
\[ \boxed{\text{Pullampara grama panchayat}} \]