How much will connections with the department chair help with grad school acceptance? As an undergraduate (not studying computer science) I was fortunate enough to work in the lab of the CS department chair at my university for an extended period of time. This work resulted in me being added as a coauthor to one of her most recent papers. She also knows me well - I took an intro CS course with her, and during my time in the lab we would be in contact practically every day. I definitely plan on asking her for a recommendation letter when I apply for graduate school in computer science next year.

Although I know that going to the same university for undergraduate and graduate school is sometimes discouraged, I would quite honestly be very happy to return there, as I very much enjoyed working under her, she is well-known in her field, and some of her research interests are very close to mine. In any event, it would be nice to have a "safety net" of sorts while exploring other options.

I know that every university has different policies about admissions decisions, so no one can speak to my particular case. But in general, how much would you say that having the backing of the department chair helps in graduate school admissions?
You're right, it's sometimes discouraged to get a graduate degree from your alma mater, but it's not as highly discouraged as getting a Ph.D. from the same place you got your master's degree. It really depends a lot on the culture of the department. When faculty are going over your letters of recommendation, test scores, and statement of intent, they're trying to mainly assess:


How likely you are to succeed in the program
How closely your interests align with faculty (i.e Can they help you? Can you help them?)


People can seem amazing on paper and turn out to be a disaster as a graduate student, and vice versa, and faculty will tell you they're taking somewhat of a gamble each year when they admit new students based on application materials alone.

If you've got someone on faculty who can vouch for your intellectual abilities and your fit factor in the department (and you clearly do), then I would say you're very likely to be in a favorable position over other applicants in that department. My department accepted a master's student who had just graduated with their bachelor's from the same department two years in a row.

As far as other programs go, it's extremely beneficial that you have co-authored a published article and would have a letter of rec from a department head. Not a guarantee, of course, but a massive help in any case.