Not the Catholic church, it started about 1700 years ago give or take a few decades. Correction, it began as scripture states in Matthew 16:18: "And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of the netherworld shall not prevail against it."
Peter was the first pope, followed by
First Century
1. St. Peter (32-67)
2. St. Linus (67-76)
3. St. Anacletus (Cletus) (76-88)
4. St. Clement I (88-97)
5. St. Evaristus (97-105)
Second Century
6. St. Alexander I (105-115)
7. St. Sixtus I (115-125)
8. St. Telesphorus (125-136)
9. St. Hyginus (136-140)
10. St. Pius I (140-155)
11. St. Anicetus (155-166)
12. St. Soter (166-175)
13. St. Eleutherius (175-189)
14. St. Victor I (189-199)
15. St. Zephyrinus (199-217)
Third Century
16. St. Callistus I (217-22)
17. St. Urban I (222-30)
18. St. Pontain (230-35)
19. St. Anterus (235-36)
20. St. Fabian (236-50)
21. St. Cornelius (251-53)
22. St. Lucius I (253-54)
23. St. Stephen I (254-257)
24. St. Sixtus II (257-258)
25. St. Dionysius (260-268)
26. St. Felix I (269-274)
27. St. Eutychian (275-283)
28. St. Caius (283-296)
29. St. Marcellinus (296-304)
All the way up to the present day.