I guess I'll be the odd man out here and have to disagree with most of you guys (respectfully).
While Rippetoe does not push the chinups into a staple (just like rows) I think if you are pushing in the vertical plane you should also pull in the vertical plane.
Imbalances in the shoulder (overactive chest, weak upper back) like internal rotation of the humerus, protracted shoulders, etc. all occur when emphasis is put on the pushing muscles, shoulder protractors and internal rotators while neglecting the antagonists.
The early stages of training like the beginning of linear progressive resistance training this balanced training is crucial to later on being victim to these imbalances.
How are the scapula retractors effectively stimulated during the routine without horizontal and vertical pulling? How are the external rotators? How are the lats stimulated directly. I think whenever there is a push there should be a pull to balance it in the same plane of motion.
We all know that retracting the scapula, externally rotating the humerus, and keeping the elbows tucked during a bench press is a recipe for maintenance of healthy shoulders; this is a principle that should be pushed more in that routine.
If you protract, you retract - balanced.
If you upwardly rotate, you downwardly rotate - balanced.
While you will most likely never maintain perfect alignment in the joints as a weightlifter, you can go to any extremes to minimize the injuries and I don't think starting strength as a routine itself takes these precautions.
If you cannot find access to a pullup station, then pulldowns could be a temporary replacement. If there's availability to pulldowns, IronGym pullup bars are very cheap and convenient. If that's out of the question, then incorporate rows at a higher frequency, but I hate to disagree here, but I feel rows and pullups both need to be mandatory if benches and overhead presses are.
A lot of assumptions, but would this work for you?
3x 5 Squat
3x 5 Bench Press
3x 5 Rows
3x 5 Squat to 75-85%
3x 5 OHP
3x 5 Power cleans
3x 8 Lat pulldowns, or BB Pullovers, or even more BB Rows, if you have no lat machine or chinup bar
This version of the routine is much greater than the routine focusing only on pulling vertically from the ground, pushing infront and upward, and squatting. This is a lot better balanced IMO. I would go with this version.