This is a rule that I was taught in my days of school, but I don't both with my students (nor, might I add, have I ever heard another teacher try to teach it). Still, I want to make it clear to anyone reading this: feel free to split your verbs and infinitives!
In case you're not sure what I mean by that, let me give an examples. For grammar sticklers, verbs such as "to love" and "to execute" must be kept together as two words, with nothing in between, to be grammatically correct. So, saying "I will faithfully love you forever," would, if we follow that, be incorrect! Clearly, these are phrases we use all the time, so let's toss that rule out!
One interesting tid-bit related to this grammar "problem" is that even President Obama has been plagued by it. When it was time for him to take his Presidential Oath in 2009, Chief Justice John Roberts, a famous stickler for grammar, could not bring himself to have Barack Obama "solemnly swear that I will faithfully execute the office of president of the United States". So, Obama instead swore to "solemnly swear that I will execute the office of president to the United States faithfully." In the end, people were worried about the legitimacy of this phrase, and Obama had to swear the original oath again later in the day.
So, go ahead and split those infinitives! We've been doing it, as authors, for ages, and the root of this rule comes from Latin, where these verbs were one word and could not be split!