Is it normal for someone who is dealing with chronic pain to become suicidal?

Unfortunately, yes. Sadly, most suicidal people choose suicide to end their pain; it all becomes too much that the idea of having to bear that for a lifetime along with bad quality of life, feeling like a burden to others becomes draining and causes further deterioration of the mental health leaving no motivation to continue living. I'm sorry if you're experiencing this, but know the pain by itself can be managed in several ways medically but what's more important to help boost the effect is a good support system who can understand you pretty well. Talk about it to people you trust, never be afraid to reach out for help when thoughts of ending it increase. Reaching out is not weak, it's bravery! You're not alone in this world and never have to deal with this on your own.