No sooner . . . . . the sun . . . . . , than the birds start chirping.

Answer: Option A

No sooner did the sun rise, than the birds start chirping.

The correct structure for this sentence is the use of "No sooner" followed by an auxiliary verb in the past tense, which in this case is "did". After "did," the base form of the verb "rise" is used. The phrase "No sooner...than" expresses that one action (the sun rising) is immediately followed by another action (the birds chirping).

Option B: is, rise is incorrect because "is" is present tense, and we need the past tense auxiliary verb "did" here.

Option C: do, rise is incorrect because "do" is used for present tense, whereas the sentence structure requires a past tense auxiliary verb.

Option D: does, rise is incorrect because "does" is used for present tense actions, but we need the past tense form to correctly match the sentence structure.

Conclusion: The correct answer is Option A: did, rise, as it correctly follows the rule of using "No sooner" with a past tense auxiliary verb and the base form of the main verb.