My approach may not be common, yet, but I guarantee patients would not only embrace the portal but they would visit frequently and interact.
Provide a simple point incentive system that is easy to understand and easy to accumulate points for healthy choices, lifestyle changes and compliance with medical directives. Set rewards for point levels such as umbrellas, t-shirts, gift cards to local establishments and have automatic entries into drawings for larger prizes at lower tiers of participation. Make awarding the winners a BIG deal around the office and with online communications to patients.
HIPAA concerns can be assuaged by stripping out health information and using patient selected usernames. The portal can be a fun, informative and valuable resource for patients and better for you a wealth of data that can be used to shape patient communication and outcomes tracking.
If you would like to learn more please reach out and I would be happy to help flesh out the concept for your practice. I have seen a variant of this in use at Orthodontic offices where children are encouraged and rewarded for specific activities beneficial to their appliances. The outcomes have been excellent.

The key here is in the question you're asking - you're wanting to motivate one "user" (the patient) for the benefit of another "user" (the physician, and/or their data mining). This is the wrong question to ask.

A more customer-centric view would be "What services can I provide through a portal, that my patients want to use?". This will vary from cohort to cohort, from disease to disease, and will likely be very specific. There is no one answer to this outside of "understand your patients" as that will drive your ability to engage with them.

I would encourage a technique like design thinking, to rapidly prototype ideas and present them to patients, to find out what motivates them, and what services they would find useful. If you crack that nut, the "encouragement" to use the portal is not needed - patients already have a tough time and anything that can make their lives easier is going to be welcome.

This isn't limited to chronic patients, the general doctor-patient relationship is extremely archaic and can benefit from a more modern approach - from booking appointments online, to completing questionnaires ahead of time, or even providing chat services for easy follow up - the possibilities are numerous.

I agree with both comments previously made. One additional consideration when thinking about the developement of the patient portal is intended outcome. Many acute environments are looking to leverage a patient portal to not only provide guidance a long their care journey, but also to reduce the number of calls that need 1:1 support through the patient services group. Additionally, provider and payers are beginning to embrace the value of the patient portal to drive health and wellness behavior This could include not only care coordination support for timely scheduling, but also wellness, diet, and speciality pharmacy support to insure protocol adherence.