Slow deploy: times-out on a hello world app.

There is a related issue #1086 which doesn't have any more activity, so I am opening a new one. I have given a super minimal application that takes over 15 mins to deploy, and most of the time times out. The slowness has gone from annoyance to blocker level for me.

How to recreate:
```
chalice new-project hello
```
edit the requirements to add
```
azure==4.0.0
```

chalice deploy takes 5, 10 or more minutes on the best case, and times out on the worst.

Recreate the report with `chalice new-project hello`, add `azure==4.0.0` to the requirements file, and run `chalice deploy`. Start by tracing the deployment path used for installing requirements and measuring where the hello-world deployment spends its time. Done means the minimal app deploys without taking over 15 minutes or timing out.

Written by the indexing model from the issue text.