There is a famous line in a famous poem (I think one can safely call
it a poem) which runs ........ "and [or 'but'] at my back I hear
time's winged chariots drawing near" .........

All I want is the complete text and the name of the author. I am
surprised that an ordinary advanced Google produces only 1, 2 or 3
references (depending on how I frame the search).

Your poem is "To His Coy Mistress," by Andrew Marvell. The reason you
were not able to find many online references is because search engines
are very literal, and a paraphrase can bamboozle them. The exact
wording of the line is "But at my back I always hear / Time's winged
chariot hurrying near."

Here is the poem in its entirety:

To his Coy Mistress
by Andrew Marvell

Had we but world enough, and time,
This coyness, lady, were no crime.
We would sit down and think which way
To walk, and pass our long love's day;
Thou by the Indian Ganges' side
Shouldst rubies find; I by the tide
Of Humber would complain. I would
Love you ten years before the Flood;
And you should, if you please, refuse
Till the conversion of the Jews.
My vegetable love should grow
Vaster than empires, and more slow.
An hundred years should go to praise
Thine eyes, and on thy forehead gaze;
Two hundred to adore each breast,
But thirty thousand to the rest;
An age at least to every part,
And the last age should show your heart.
For, lady, you deserve this state,
Nor would I love at lower rate.

But at my back I always hear
Time's winged chariot hurrying near;
And yonder all before us lie
Deserts of vast eternity.
Thy beauty shall no more be found,
Nor, in thy marble vault, shall sound
My echoing song; then worms shall try
That long preserv'd virginity,
And your quaint honour turn to dust,
And into ashes all my lust.
The grave's a fine and private place,
But none I think do there embrace.

Now therefore, while the youthful hue
Sits on thy skin like morning dew,
And while thy willing soul transpires
At every pore with instant fires,
Now let us sport us while we may;
And now, like am'rous birds of prey,
Rather at once our time devour,
Than languish in his slow-chapp'd power.
Let us roll all our strength, and all
Our sweetness, up into one ball;
And tear our pleasures with rough strife
Thorough the iron gates of life.
Thus, though we cannot make our sun
Stand still, yet we will make him run. 

Luminarium: To His Coy Mistress
http://www.luminarium.org/sevenlit/marvell/coy.htm

Google search strategy:

Google Web Search: "time's winged OR wingèd chariot"
://www.google.com/search?hl=en&ie=UTF-8&q=%22time%27s+winged+OR+wing%C3%A8d+chariot

I hope this helps. If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

Anyone who awards any service - anywhere - with five stars, and
immediately suggests how to make improvements would be a ripe nut. BUT
if Google programmers can find a way of insinuating dedicated
detection for "Literature, Poetry, and Quotations" [in Advanced Search
fields] it really would be great!
I guess it would "simply" mean tagging all such online material and
using a less bamboozling searchlight. A laser, perhaps?  :-) Many
thanks. <br> Andrew Marvell indeed! It is a good feeling to read
something once again after a lapse of half a century - like meeting a
very long lost friend. Many thanks to you, pinkfreud-ga! Love the
name! You don't need no ejjercation - but you certainly ain't just a
bwick in de war! Oh dear. Damn those chariots! (I *thought* the word
was hurrying and seem to remember my English master rambling on about
it lending a touch of onomatopoeia to help one hear the chariots. In
retrospect,  I must have felt my teacher - the serendipitously named
Mr. Maybe, who always smelled faintly of Dettol - an Englishman
teaching in Australia in the early 50s. - a strange man with an even
stranger wife - immediately became more interested in the concept of
onomatopoeia than in the Mr. Marvell's Mistress. Pinkfreud! Hah! Love
it. BTW it seems I am registered here (don't remember doing it) with
another '-ga' suffixed username. I saw it just now. At first glance, I
really couldn't make head nor tail of it.  Quitega-ga. It threw me
with its somewhat Aztec features and only after twigging your own
ga-name
did I recall . . . after a mere 50 years . . . that I am indeed quite ga-ga! :-)

Many thanks for the five stars and the tip!

I, too, am quite ga-ga after more than 50 years. 

I believe my ga-gariousness is probably due to "hardening of the smarteries."

Best,
pinkfreud

My God what a run-around. Password? What password? Had to go and find
out how to change it in the end. All of it, in fact. I began by trying
to find a way of doing what I am now doing - adding a comment. A

t one stage of the game I came to that page where you have to sign
your life away and donate millions to geniuses who might well live
better on bread and cheese and vinho da meja in a converted Algarve
windmill. It's fun. Try it!

Anyway . . . I just want to let you know - I blush - that only *after*
writing earlier did I see that EVERYONE in these yer partz has a name
with a "-ga" suffix, which is terrible. Why? Well, I can't remember
whether - at the time
I chose the extraordinary - even for me - username "Quitega" -
whether, at that time, I already knew that it would be suffixed with a
"ga" - or not!

Serendipity? Prescience? I worked out - quite quickly in this past
hour - with  time's winged charriots hurrying, flurrying, snorting,
flapping and currying by in an vast endless hordes - that the suffix
stands for Google Answers. I must admit, though, that I did waste a
nanosecond or two pondering if it was "ga" as in Garfield or "ga" as
in "hay".   =(:-o

I managed - before having to change my password for arcane Googlic reasons - 
to see your sort of "bio". You've answered something like 1,000 questions, 
I think it was, and only had to make five refunds. 

I'd give anything to know the details!  :-)  Pleeeeeeaaaaasssse?! 

Thanks for hardening of the smarteries. First time! HILARIOUS!
Beats "old-timers" into a cocked hat.  Original? I wouldn'r be 
surprised. Thanks again. TTFN. 
John.