How to get a smooth paste from ground chickpeas?

You cannot make good hummus from canned chickpeas, you should make it from fresh dried beans

The beans need plenty of soaking and rinsing

When cooking, add one tsp of baking soda per cup of beans. Baking soda chemically softens the bean proteins. Never add salt or other flavourings during the bean cooking stage

Traditional hummus is somewhat coarse, but very soft (due to baking soda). It is made with a minimal amount of olive oil, but drizzled with olive oil and a sprinkle of cooked, and still warm chick peas when served

Restaurant hummus is often just over processed junk made in a factory with a commercial grinder (like a peanut butter grinder)

Also, see How should I prepare dried chickpeas? if your chickpeas never go soft

I make hummus often, too, and I've used an immersion blender, mini food processor, and blender. The secret to getting a smooth hummus, regardless of the tool, is using plenty of olive oil but adding a small amount of water to make it easy to blend thoroughly. I use about 1/4 - 1/3 cup of olive oil per batch (with one 16-oz. can of chickpeas, rinsed and drained), and add a splash of water at a time while blending, until I achieve the desired consistency. (The other wet ingredients I use are about 3 tablespoons of tahini and 1 tablespoon of lemon juice.)

Since you didn't post your recipe, I'm not sure what your ingredients are, but if adding water makes your hummus too watery, I'd try increasing the amount of oil.

In addition to TFD's answer, I'd like to add that I use an indian food grinder, rather than a food processor or blender, to puree dips like hummus and baba ganouj. It does a vastly better job than a food processor does.

Sorry, canned garbanzos can work too. Drain the beans, put in a blender or food processor with a small amount of chicken stock or liquid from a can. Season with salt, pepper, cayenne, garlic powder, and cumin to taste. Blend till smooth and serve in a bowl with drizzle of olive oil. Easy and yum.

The coarse paste texture suggest that the hummus does not have enough moisture. You can correct that situation either by adding more olive oil or adding more water. Oil will add more flavor, but water will make for a more healthful result. I tend to compromise by adding the amount of olive oil called for in the recipe, then drizzling in water a little at a time until I get the consistency I want.

I'd suggest soaking the hummus overnight with a very small amount of bicarb soda (maybe a 1/4 teaspoon), adding the same amount when cooking. If you can be bothered peel the skin and grind when the chickpeas are still warm.

For a whiter hummus, blend the tahini and lemon juice first before adding the other ingredients. Reserve some of the cooking fluid and add it in if required to achieve a smooth paste. You shouldn't need to add any olive oil to the hummus, it's traditionally drizzled on top, not added to the mix.

I feel that machine blending adds much air and 'fluffiness' to hummous and should be kept to a minimum by thorough cooking.

The goal should be whole yet completely tender beans. Slow cooking in slightly alkaline water, as suggested above with soda, gives best results. Slowing the soaking by using cold water overnight in fridge often helps prevent splitting and exploding.

Sieving out hard bits after blending is time-consuming but will give that extra smoothness.

If there are still troubles, you're not crazy: different crops and storage time all affect results. The complicated chemistry of beans keeps food scientists busy! Try a different batch.

Sorry to all the purists, but the best trick is to mix equal amount chickpeas and a small white bean like navy beans. The taste is not noticeably different, but much, much smoother.