46 consecutive checks in a legal game:
[Event "?"]
[Site "?"]
[Date "2007.08.11"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[ECO "E32"]
1. h4 g5
2. a4 b5
3. c4 d5
4. cxd5 bxa4
5. Ra3 gxh4
6. g4 f6
7. g5 h3
8. g6 h2
9. d4 a5
10. Bg5 fxg5
11. f4 g4
12. Nh3 g3
13. Nf2 g2
14. g7 h5
15. b4 Nh6
16. g8=R g1=Q
17. Kd2 Rh7
18. Rh8 Kd7
19. f5 Nc6
20. Rg3 a3
21. Nc3 a2
22. d6 a4
23. b5 Ra5
24. b6 Re5
25. b7 Na7
26. b8=Q Kc6
27. d7 Qe8
28. d8=Q Qf7
29. d5+ Kc5
30. d6 Kd4
31. d7 Bb7
32. Qdc8 h4
33. Bg2 Re3
34. d8=Q+ Ke5
35. f6 Rg7
36. Be4 Rg4
37. Bb1 Qh7
38. f7 Bg7
39. f8=Q a3
40. Nfe4 a1=Q
41. Kc2 h3
42. Kb3 a2
43. Kc4 Qb2
44. Qfe8 Bc6
45. Qa6 Kf5
46. Kc5 Bd5
47. Qb4 Bf7
48. Qdb8 Bh5
49. Qf1+ Qf2
50. Qg2 a1=N
51. Rd1 h1=Q
52. Rd3 Qhc1
53. Qba3 h2
54. Qbb4 h1=Q
55. Qba5 Qb8
56. Q5b6 Qh4
57. Qec6 Qfg1
58. Rd4 Qgh1
59. Nf2+ Rge4
60. Kd5 Ng4
61. Ra4 Qg6
62. Ncd1 Bb2
63. Qab4 Ba3
64. Ra5 Rb3
65. Nb2 Qh7
66. Qf1 Qg6
67. Nbd3 Qh7
68. Rf8+ Bf7+
69. Rxf7+ Qxf7+
70. Qe6+ Rxe6+
71. Rf3+ Qxf3+
72. e4+ Rxe4+
73. Qe6+ Rxe6+
74. Qe4+ Rxe4+
75. Qe6+ Rxe6+
76. Kd4+ Nb5+
77. Rxb5+ c5+
78. Nxc5+ Re4+
79. Ncxe4+ Bc5+
80. Nxc5+ Qd3+
81. Ncxd3+ Qe5+
82. Nxe5+ Nc2+
83. Bxc2+ Rd3+
84. Nexd3+ Qd5+
85. Rxd5+ e5+
86. Rxe5+ Nxe5+
87. Ng4+ Qf2+
88. Qxf2+ Nf3+
89. Qxf3+ Qf4+
90. Qe4+ Qxe4+ *
It is known that an infinite sequence of consecutive checks is impossible.