Splitting an infinitive (placing an adverb between 'to' and the verb, like 'to boldly go') is grammatically incorrect in English.
The prohibition against split infinitives is a false rule invented in the 19th century by grammarians who imposed Latin grammar onto English. In Latin, infinitives are single words and cannot be 'split,' so when Latin-worshipping educators tried to apply this logic to English, they created an artificial constraint. English infinitives are two-word phrases, and adverbial modification between them is grammatically sound and often produces the most natural phrasing. Major style authorities (Merriam-Webster, Oxford, APA) now explicitly permit and sometimes prefer split infinitives for clarity and rhythm. 'To boldly go where no one has gone before' is not merely acceptable, it's better than the awkward alternatives 'to go boldly' or 'boldly to go.'