Hot on the heels of today's Microsoft buys a share of Facebook announcement comes some speculation from Search Engine Land, that Live Search may soon make an appearance inside of Facebook.  The speculation, from Greg Sterling:

During this afternoon's Microsoft-Facebook conference call the question was asked whether the new deal would include paid search. Microsoft's Kevin Johnson and Facebook's Owen Van Natta declined to directly answer the question and made general statements about future collaboration and that the deal a "win win win." Nobody listening was really all that clear on what it might mean as a practical matter beyond traditional display ads and hypothetical Facebook-specific ad types soon to be announced.

However if one steps back it seems that one thing is fairly certain: A Live Search box and related ad inventory is almost sure to make its appearance on Facebook in the near term.

Sterling goes on to describe how Facebook is without web search from within the application, and that both MySpace and Bebo utilize search bars.  While it may be going pretty far out on a limb to say "one thing is fairly certain", including Live Search in Facebook would seem to be a positive move for both sides.