What is the grammar in this sentence?

A phrase like

…, sie heute noch zu bekommen

can be referred to as uneingeleiteter Infinitivsatz (infinitive clause without subjunction). In

… die Chance, sie heute noch zu bekommen

it is used attributiv (attributively, like a relative clause is). Uneingeleitete Infinitivsätze, however, can also be Inhaltssätze, i.e. serve as the subject or object of another sentence:

• Sie heute noch zu bekommen ist unmöglich (Subjektsatz)
• Ich glaube, sie heute noch zu bekommen (Objektsatz)

All Infinitivsätze have in common that they have no subject and obiously no finite verb.

Oftentimes, Infinitivsätze can be transferred into dass-clauses and vice versa. However, in both directions it's not always possible. This, e.g., was asked here.