I feel it is fair to say that a number of blue chip shares have let investors down over the last few years.

Investments in a blue chip share such as BHP Billiton Limited (ASX: BHP) would have lost you money whether you had held it for one, three, five, or even ten years. The surprising thing about this statistic is that it includes the generous dividend it has been paying out all this time as well.

It is a similar story for Woolworths Limited (ASX: WOW), with shareholders that have been invested in it for the last five years coming out with a loss also.

But many of those savvy investors that looked beyond blue chips and delved deep into the market have come out with impressive gains. In fact, some small cap shares of yesteryear are the blue chips of today.

The one I like to mention is TPG Telecom Ltd (ASX: TPM). Back in 2006, TPG Telecom was a small cap share with a market capitalisation of $320 million. Fast-forward to today and it’s now a blue chip share with a market capitalisation of over $10 billion dollars.

If you had invested $50,000 in TPG Telecom shares back in 2006 that investment would be worth almost $1.3 million today, thanks to its average annual total shareholder return of 38.1% over the last 10 years.

This just goes to show that if you can unearth a future blue chip share whilst it’s still small, you could make yourself very rich. This is of course easier said than done. But to help you on your way I have picked out three small cap shares which I believe could grow to be many times their current size. Here they are:

Altium Limited (ASX: ALU)

Altium is a company that looks set to profit from the phenomenal growth of the internet of things market, which Cisco predicts will be worth US$14.4 trillion by 2022. Altium’s software enables companies to design printed circuit boards to be used in connected devices. I believe that thanks to the expected growth of its addressable market there is every chance Altium will deliver solid results that produce strong returns for shareholders over the next decade.

Medical Developments International Ltd (ASX: MVP)

Medical Developments International may not be a familiar name, but many will know its pain-management product Penthrox. It has been used for decades by the defence force, ambulance officers, and surf lifesavers. Penthrox is a pen-shaped device designed to deliver rapid pain relief through the inhalation of methoxyflurane. The company has ambitions to make Penthrox a mainstream analgesic of choice around the world, and is making good progress in doing so. The first half of FY 2016 saw Penthrox receive approvals in the United Kingdom, Belgium, Ireland and Singapore. The big market will of course be the United States, and by the end of June it expects to have received feedback from the US Food and Drug Administration. If it satisfies the FDA’s requirements and Penthrox is able to go on sale in the USA, then I would expect to see the company’s sales get a huge boost. The company is cash flow positive and looks set to have a bright future, in my opinion.

REVA Medical Inc (ASX: RVA)

REVA is a clinical stage medical device company that has developed bioresorbable scaffolds which are an alternative to traditional metal stents. Metal stents are permanently implanted into an artery to treat coronary artery disease, whereas REVA Medical’s bioresorbable scaffolds are designed to disappear naturally over a period of time. Its clinical trials have been positive and management looks to be positioning the company and its scaffolds well in a global coronary stents market which is expected to be worth US$8.3 billion per year by 2019. With a market capitalisation of $450 million, I believe REVA has a lot of growth ahead of it.

Foolish takeaway

I believe these three shares offer investors the potential for strong growth in the future. But it is worth remembering that for every TPG Telecom that transitions successfully from a small cap to a blue chip share, there are countless others that don’t make it.

As well as these three small caps, I believe it would be well worth investors taking a look at these three "new breed" blue chip shares which could provide share price gains and a solid dividend in the months ahead.

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Motley Fool contributor James Mickleboro has no position in any stocks mentioned. The Motley Fool Australia owns shares of Altium. 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. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson. I contribute to The Motley Fool as a freelance writer and the thoughts and opinions in this post are my own, not that of The Motley Fool’s.