When the Going Gets Tough... (Exodus 6:2-27)

This past Sunday I had the privilege of preaching at Christ's Covenant Church. I continued our series in Exodus, which is entitled "From Slavery to Sonship." You can find the audio of the message here.

Christ as the Rock of Exod 17 (1 Cor 10:1-4)?

In 1 Cor 10:1-4, Paul makes the shocking claim that the rock from which the Israelites drank in desert (Exod 17) was Christ:

For I do not want you to be unaware, brethren, that our fathers were all under the cloud and all passed through the sea; and all were baptized into Moses in the cloud and in the sea; and all ate the same spiritual food; and all drank the same spiritual drink, for they were drinking from a spiritual rock which followed them; and the rock was Christ.
(1 Cor 10:1-4; NAS1995)

On what basis does Paul make such an identification? Is this merely fanciful exegesis? Is there any theological basis for such an identification?