It is possible to train to both litter box (or pee pads) and outside. My Jasmine does both. When I'm home, I take her outside frequently and she will use the bathroom outside. When I am away or during the night, she will use her pee pad. So it is possible to do both.
How old is your chi? Jasmine is 9 months old now, and I didn't start trying to train her to go outside until she was almost six months. My theory (and it is just my theory), is to train to one thing at a time. In other words, I didn't start training Jasmine to go outside until I was completely sure she was consistently going potty on her pad, as I felt it would be too confusing to train for both at one time.
Is there not some place downstairs where you could have a litter box that would be out of sight to most? Or how about trying a pee pad if you think she would use it.
Whatever you decide, good luck, and remember consistency and patience are the keys.