A chronic condition is one that persists for a long time. Asthma is a chronic condition: if you have asthma today, then you almost certainly had asthma yesterday and will still have it next week. Source and more details: Medline, OED.
Acute has two relevant meanings. In colloquial usage, it just means severe; so in that sense, a condition can be both acute and chronic. However, in medical language, it is specifically used in contrast to chronic; an acute condition, in this sense, is something which by its nature is (expected to be) of limited duration; something which develops over a short timescale. So in this technical sense, a condition cannot be both acute and chronic. An asthma attack is acute in this sense: it’s a temporary flare-up of the underlying chronic condition. Source and more details: Medline, OED.
Obtuse is essentially irrelevant to these medical usages; it was used in a comparable sense in the past, but this usage is now extremely rare (OED; Google ngrams). In mathematics, however, it is still used in contrast to acute. An acute angle is one measuring less than 90°, while an angle more than 90° (but less than 180°) is obtuse.