"chance of" vs "chance to"

"chance of" is typically used when "chance" means "likelihood", "probability", "odds".
"chance to" is typically used when "chance" means "opportunity".

"intention of" is very often used in the negative expression "to have no intention of"
"intention to" is always used with "expletive 'it'", thus: "It is [my / your / his / ...] intention to ..."

There's more to be said, but I think these rules of thumb will give you a good start. Here's some examples of the principles stated above:

What is the [chance / likelihood] of finding a four-leaf clover in this field?
ALSO, "What are [the / my] [chances / odds] of finding a four-leaf ...?"
[There's / You have] no chance of winning the lottery if you don't buy a ticket.

I had [a chance / an opportunity] to meet Sophia Loren when I visited Italy.
Have you had [a chance / an opportunity] to talk to the new boss yet?

Maria had no intention of responding to the letter.
I'm so sorry! I had no intention of spoiling your fun.

It is not my intention to teach physics next year.
Is it your intention to get married soon?

Hope that helps!

"... will be an enormous benefit ..." is a perfectly good way to say it.

There are several ways to approach expressions of this form.

1. "to be" + "of"-phrase can sometimes be paraphrased with the verb "to have".

This package is of the same weight as the other.
= This package has the same weight as the other.
The syntax was of the form SVO. = The syntax had the form SVO.

2. In the same way that the adjective "big" operates in a., below, an "of"-phrase, too, can operate as an adjective, as in b. Note the repetition of the subject noun in the predicates.

a. That man is big. = That man is a big man.
b. The instructions were of great help. = The instructions were instructions of great help.

This fabric is of the highest quality.
This fabric has the highest quality. (from 1.)
This fabric is fabric of the highest quality. (from 2.)

3. The "of"-phrase is frequently simply synonymous with an adjective.
Specifically, the standard formula "of" + "adjective" + "noun" so often found after "to be" is very frequently equivalent to "adverb" (from the original adjective) + "adjective" (from the original noun).

"to be:"
"of enormous benefit" = "enormously beneficial"
"of utmost importance" = "extremely important"
"of no significance" = "not significant"
"of unparalleled value" = "valuable without parallel" = *"unparalleledly valuable" (Sometimes the adverbial part cannot be expressed with a single-word adverb!)
"of little use" = "not very useful"
"of sturdy construction" = "sturdily constructed"

Maybe thinking of the "to be" + "of"-phrase structures in one of these ways (or in other similar ways of your own invention) will help you to become more comfortable with them.

In these constructions the "of" connects a 'deverbal noun' to its object, sometimes its subject.

"West Brom complete the signing of Chaplow" is like "West Brom complete this: West Brom signs (up) Chaplow. "

"sign" and "signing" are different and cannot be interchanged.

Here's another example:

"I completed the homework" can be changed to "my completion of the homework" and then used in a bigger sentence: "My completion of the homework was not enough to please the teacher."

Note how "completion" is a noun that comes from the verb "complete". By removing the verb quality from it and making it a noun, we make it a 'deverbal' noun, a noun formed from a verb.

The "-ing" and "-tion" endings are very frequently the sign of a deverbal noun, but sometimes the verb and the noun are spelled exactly the same, and sometimes other changes occur.

Here are some "verb : deverbal noun" pairs.

complete : completion
drink : drinking
understand : understanding
evaluate : evaluation
defend : defense
love : love
sign : signing
fear : fear

Now here are some verb phrases and corresponding noun phrases that use the examples above:

to complete the assignment : the completion of the assignment
to drink coffee : the drinking of coffee
to understand the principles : understanding of the principles
to evaluate the contestants : the evaluation of the contestants
to defend the client : defense of the client
to love music : the love of music
to sign Chaplow : the signing of Chaplow
to fear snakes : the fear of snakes

That's just a start, but maybe it will help answer your question.

CJ

Guest, It was just to show that "the" is not a required element of the structure. To illustrate it better I probably should have shown some of the examples with "the", some with "a", some with "my", and so on, as well the ones without a determiner. Sorry if I confused you somehow. Jim