The ability to support a rising dividend year in and year out is one of the rarest but most prized attributes of publicly traded companies among dividend investors. In addition to the income enjoyed by shareholders, such an ability also says something about the likelihood that a company's shares will appreciate over the long term. A corporation without steadily climbing earnings won't be able to support a rising dividend over a period of many years. And sooner or later, that earnings power should be reflected in the stock price.  

If you're looking for high-quality companies that also exhibit dividend-increase longevity, Dividend Aristocrats form an attractive pool to choose from. A Dividend Aristocrat is defined as a company that has raised its dividend for at least 25 consecutive years. We checked in with three of our analysts for their best current Dividend Aristocrat investment candidate. They returned three stock picks from an even more exclusive list, the S&P 500 Dividend Aristocrats. You can read their thoughts on these blue-blooded dividend payers below:

Liquified natural gas carrier owned by Chevron Corp., with superimposed Chevron logo over image. Source: Chevron 2014 annual report.

Adam Galas
I think the oil crash presents a great long-term opportunity for dividend lovers to pick up undervalued shares of Chevron Corp. (NYSE:CVX), which has raised its dividend every year since 1986.

More impressively, Chevron's dividend growth rate hasn't been some token tiny amount designed to obtain and keep the company's status as a Dividend Aristocrat.

CVX Quarterly Dividend data by YCharts.

Boasting some of the best management in the oil industry, Chevron has been able to grow, prosper, and reward long-term income investors with 7% CAGR dividend growth for three decades that include no fewer than six oil crashes.

So Chevron has plenty of experience when it comes to sustaining dividend growth during times of immense industry distress. Its management is cutting costs to the bone, with 2016's capex budget 25% below 2015's. Should oil prices remain low for several years, Chevron has identified ways to lower that another 20% by 2018.

In addition to cost cuts, the company's refining operations are benefiting from the steep drop in oil prices. Crude oil is obviously the main input for refined products, but it isn't the only one, and as oil prices have fallen, refining margins have expanded. This serves as a natural hedge against its primary business: oil production. In fact, in the first nine months of 2015, Chevron's refining profits are up 134% to $6.6 billion.

The company is also selling a lot of non-core assets and refocusing its future production investment on key growth opportunities such as offshore drilling in the Gulf of Mexico and LNG projects in Australia. Thus far in 2015, Chevron has sold $5.4 billion in assets and plans to sell another $5 billion to $10 billion through 2017.

Finally, the company can and is raising large amounts of cheap debt -- $8 billion in the first three quarters of 2015. Luckily, Chevron's conservative, long-term-minded management has kept the company's balance sheet strong even during the boom times. Thus its AA credit rating and much lower debt levels relative to its competitors means it can borrow enough cash to keep growing the dividend during the lean years.

Dan Caplinger
The power of dividend growth is a huge component of what makes stocks such an attractive long-term investment, and that's especially true among blue-chip stocks like energy giant ExxonMobil (NYSE:XOM). It's easy to lose sight in the middle of an energy bust of just how strong Exxon has been over time, but when you look at the stock's nearly 12.5% average annual total return since 1985, Exxon's profit potential becomes clearer -- as does the role that its 3.5% dividend yield plays in producing that total return.

For 33 straight years, ExxonMobil has found ways to boost its dividend in good times and in bad. That has included several bear markets for oil in the past, and just this past May, Exxon paid a 6% higher dividend despite one of the steepest plunges in oil prices in recent memory. Even with earnings having fallen sharply, Exxon makes enough money to finance dividend payouts at current levels. Over time, investors can expect the oil giant to find ways to profit from changing energy markets just as it has for decades, and steady income growth will play its part in keeping shareholders satisfied over the long run.

Asit Sharma
I agree with Dan that dividend growth is a compelling reason to hold stocks in your portfolio over a long time horizon, and I'm a great believer in dividend reinvestment (for those who don't need to cash dividend checks for current income). S&P 500 stalwart 3M Co. (NYSE:MMM) is a stable and growing investment vehicle offering a generous current dividend yield of 2.9%.

Like Chevron and Exxon, 3M hasn't had a great year, but for a very different reason than the current oil glut. As a U.S.-based multinational, 3M's revenue and earnings have been undermined by an extremely strong U.S. dollar in 2015. In its most recently reported quarter, foreign currency translation proved a 7.4-percentage-point drag on total company revenue of $7.7 billion. Currency woes also reduced final pre-tax earnings of $1.8 billion by $95 million.  

Even under currency pressure, 3M has managed to increase its operating margin by roughly 100 basis points through the first three quarters of this year. It's also very focused on maintaining its excellent free cash flow generation. The company is on a pace to generate free cash flow (operating cash flow after fixed asset expenditures) in the range of 95%-100% of projected net income for the year. 

This efficient cash generation is a hallmark of 3M, and the company places a high priority on returning cash to shareholders. Currently, its shareholder return streak consists of 98 straight years of issuing a dividend, with dividend increases in each of the last 57 years.

In 2015, 3M has combined this long-term stability with some near-term belt tightening. In its current lower earnings environment, it's pragmatically reducing worldwide head count by about 1,500 employees, for an estimated savings of $130 million in 2016. It's also divesting a few non-core businesses within the company's "Safety and Graphics" group. This well-run diversified industrial conglomerate is heading proactively into the new year, and should be able to keep its aristocratic status for many more years into the future.

Adam Galas has no position in any stocks mentioned. Asit Sharma has no position in any stocks mentioned. Dan Caplinger has no position in any stocks mentioned. The Motley Fool owns shares of ExxonMobil. The Motley Fool recommends Chevron. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.