आग्निवेश्यादाग्निवेश्यो गार्ग्याद्गार्ग्योगार्ग्याद्गार्ग्यो गौतमाद्गौतमः सैतवात्सै-तवः पाराशर्यायणात्पाराशर्यायणो गा-र्ग्यायणाद्गार्ग्यायण उद्दालकायनादुद्दाल-कायनो जाबालायनाज्जाबालायनो मा-ध्यंदिनायनान्माध्यंदिनायनः सौकराय-णात्सौकरीयणः काषायणात्काषायणःसायकायनात्सायकायनः कौशिकायनेः-दधीच आथर्वणाद्दध्यङ्ङाथर्वणोऽथर्वणो दैवादथर्वा दैवो मृत्योः प्राध्वंसनान्मृत्युः प्राध्वंसनः प्रध्वंसनात्प्रध्वंसन एकर्षेरेकर्षिर्विप्रचित्तेर्विप्रचित्तिर्व्यष्टेर्व्यष्टिः सनारोः सनारुः सनातनात्सनातनः सनगात्सनगः परमेष्ठिनः परमेष्ठी ब्रह्मणो ब्रह्म स्वयंभु ब्रह्मणे नमः ॥ ३ ॥
In plain words
The names run on, each teacher naming the one before him: from Āgniveśya to Gārgya, Gārgya to Gārgya, on through Gautama, Saitava, Pārāśaryāyaṇa, Gārgyāyaṇa, Uddālakāyana, Jābālāyana, Mādhyaṃdināyana, Saukarīyaṇa, Kāṣāyaṇa, and Sāyakāyana, down to Kauśikāyani and Dadhīca, to Dadhyañc the son of Atharvan, to Atharvā of the line of Daiva, to Mṛtyu and Prādhvaṃsana, to Pradhvaṃsana, Ekarṣi, Vipracitti, Vyaṣṭi, Sanāru, Sanātana, and Sanaga, until the chain reaches Parameṣṭhin -- and Parameṣṭhin received it from Brahman itself, the self-existent, needing no source beyond itself. To that Brahman, homage.
Close to the Sanskrit
From Āgniveśya, Āgniveśya; from Gārgya, Gārgya; from Gārgya, Gārgya; from Gautama, Gautama; from Saitava, Saitava; from Pārāśaryāyaṇa, Pārāśaryāyaṇa; from Gārgyāyaṇa, Gārgyāyaṇa; from Uddālakāyana, Uddālakāyana; from Jābālāyana, Jābālāyana; from Mādhyaṃdināyana, Mādhyaṃdināyana; from Saukarāyaṇa, Saukarīyaṇa; from Kāṣāyaṇa, Kāṣāyaṇa; from Sāyakāyana, Sāyakāyana; from Kauśikāyani, Dadhīca; from Ātharvaṇa, Dadhyañc Ātharvaṇa, Ātharvaṇa; from Daiva, Atharvā Daiva; from Mṛtyu and from Prādhvaṃsana, Mṛtyu, Prādhvaṃsana; from Pradhvaṃsana, Pradhvaṃsana; from Ekarṣi, Ekarṣi; from Vipracitti, Vipracitti; from Vyaṣṭi, Vyaṣṭi; from Sanāru, Sanāru; from Sanātana, Sanātana; from Sanaga, Sanaga; from Parameṣṭhin, Parameṣṭhin; from Brahman, Brahman, the self-existent -- homage to Brahman.