Infinitives and Superlatives

Superlatives can be followed by infinitive structure.

This structure is also common with first, second, third etc, next, last and only.

• Who was the first person to climb Everest without oxygen? 
• The next to arrive was Mrs Patterson. 
• She's the only scientist to have won three Nobel prizes. 
• She’s the youngest person ever to swim the Channel. (= ... the youngest person who has ever swum ...)

This structure is only possible when the noun with the superlative has a subject relationship with the infinitive. 

Is this the first time that you have stayed here?
(NOT...the first time for you to stay here: time is not the subject of stay.)

[source: Practical English Usage]