The 30-year-old woman, who runs a mountain hut for climbers, started to have preterm contractions early on Tuesday morning but due to bad weather an emergency helicopter could not rescue her.
Instead a team of 15 climbers, including a mountain rescue doctor and a gynaecologist, climbed up to meet her and then took her downhill to a mountain pasture in Kartisch.
Even then the conditions were still too bad for the helicopter to attempt a safe landing, and the woman gave birth at 5pm, at 2,250 metres above sea level. By 6pm the weather had improved and mother and baby were flown to hospital in Lienz. They are reported to be in a stable condition.
In related news, the birth rate in Austria has increased slightly compared to the first half of 2013, with an average increase of 3.1 percent.
From January to June 2014 more births were registered, especially in Upper Austria (up 8.1 percent), in Salzburg (plus 7.7 percent) and in Vorarlberg (plus six percent).
Rising birth rates were also seen in Lower Austria (up 3.8 percent), in Vienna (plus 3.7 percent), in Styria (plus one percent), in Tyrol (plus 0.7 percent) and Carinthia (+0.4 percent).
The only province which is bucking this trend is Burgenland, which saw a decline in its birth rate. Get on the job, Burgenland, you're letting the side down.