Ah! I love this question! In fact, I used to do a few 'in the chair' exercises when I was bound to an office.
From the chair:
-Dips. If the chair has arms and they are strong enough, use the arms with your feet on the ground. If you really trust the arms, put your feet on the desk!
If the chair has no arms or you don't trust them, do bench dips (see: https://hubpages.com/health/Great-Workouts-to-Buil... for instructions.)
-Straight leg lifts from the chair, or knee lifts. Sit in the chair, extend your legs and lift them up to a 45 degree angle (or a little lower.) For knee lifts, bring your butt to the edge of the chair, squeeze your knees together and try to touch them to your chest.
-If you don't mind getting on the floor, do pushups or leg lifts or any bodyweight exercises from here. If you have to use the office chair, put your hands on it and do incline pushups or tricep extensions.
-Have a strong doorframe with a bit of a ledge? If you are strong enough and the ledge is wide, do finger pullups. If you need an assist, stand on the chair to make it easier. You can also look in the parking area and sometimes the stairwell for a pullup bar substitute.
You can also bring some resistance bands or small dumbbells with you, depending on your office environment. A couple of short exercise sessions throughout the day is a great way to stay sharp and feel great. Good luck!