When the monarch caterpillar has completed 5 instars (molting due to growth), it will usually wander away from the milkweed and find a spot to transform into chrysalis. This picture is nice because it shows one of our little guys after about the 3rd instar. The larger one below probably after the 4th or 5th. It is hard to keep up with them. All of this growth happens within about 10 days. They go from about 1mm to about 2 inches!
When we had caterpillars before, we would have to search the whole screened porch to locate the chrysalis because it usually happened when we were not there. Many times it was under a piece of furniture. This time we were blessed as the caterpillar stayed on the milkweed.
Before the caterpillar transforms, it will attach its rear to an object using silk like threads. Once that is secure, it will hang down in a "J" formation.
He is still rather tightly curled in this photo, but soon he will hang into a clear "J" form, the antenna will go limp and he will gradually transform into a chrysalis. After that the last molt occurs revealing a "jewel of nature in jade and gold". (I borrowed that phrase from Anna Comstock's book). :-)
Here is a link if you'd like to watch the process. It is fascinating to me.